Multipele Regressie Analyse

*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, 16 Dec 2009 06:11:02 -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/Dec/16/t1260970123qmktnmnv6zaok3p.htm/, Retrieved Wed, 16 Dec 2009 14:28:55 +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/Dec/16/t1260970123qmktnmnv6zaok3p.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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95.1 136 97 133 112.7 126 102.9 120 97.4 114 111.4 116 87.4 153 96.8 162 114.1 161 110.3 149 103.9 139 101.6 135 94.6 130 95.9 127 104.7 122 102.8 117 98.1 112 113.9 113 80.9 149 95.7 157 113.2 157 105.9 147 108.8 137 102.3 132 99 125 100.7 123 115.5 117 100.7 114 109.9 111 114.6 112 85.4 144 100.5 150 114.8 149 116.5 134 112.9 123 102 116 106 117 105.3 111 118.8 105 106.1 102 109.3 95 117.2 93 92.5 124 104.2 130 112.5 124 122.4 115 113.3 106 100 105 110.7 105 112.8 101 109.8 95 117.3 93 109.1 84 115.9 87 96 116 99.8 120 116.8 117 115.7 109 99.4 105 94.3 107 91 109

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation tip[t] = + 125.473162851457 -0.166433095863777wrk[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) 125.473162851457 7.238963 17.333 0 0 wrk -0.166433095863777 0.058681 -2.8362 0.006246 0.003123 Multiple Linear Regression - Regression Statistics Multiple R 0.346385423504831 R-squared 0.119982861616621 Adjusted R-squared 0.105067316898258 F-TEST (value) 8.04414883144772 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.00624551065182088 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.62127595594055 Sum Squared Residuals 4385.25754740024 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 102.838261813984 -7.73826181398391 2 97 103.337561101575 -6.33756110157521 3 112.7 104.502592772622 8.19740722737837 4 102.9 105.501191347804 -2.60119134780429 5 97.4 106.499789922987 -9.09978992298695 6 111.4 106.166923731259 5.23307626874061 7 87.4 100.008899184300 -12.6088991842997 8 96.8 98.5110013215257 -1.71100132152569 9 114.1 98.6774344173895 15.4225655826105 10 110.3 100.674631567755 9.62536843224522 11 103.9 102.338962526393 1.56103747360747 12 101.6 103.004694909848 -1.40469490984765 13 94.6 103.836860389167 -9.23686038916654 14 95.9 104.336159676758 -8.43615967675785 15 104.7 105.168325156077 -0.468325156076737 16 102.8 106.000490635396 -3.20049063539562 17 98.1 106.832656114714 -8.73265611471451 18 113.9 106.666223018851 7.23377698114928 19 80.9 100.674631567755 -19.7746315677548 20 95.7 99.3431668008446 -3.64316680084456 21 113.2 99.3431668008446 13.8568331991554 22 105.9 101.007497759482 4.89250224051768 23 108.8 102.67182871812 6.12817128187990 24 102.3 103.503994197439 -1.20399419743898 25 99 104.669025868485 -5.66902586848541 26 100.7 105.001892060213 -4.30189206021296 27 115.5 106.000490635396 9.49950936460438 28 100.7 106.499789922987 -5.79978992298695 29 109.9 106.999089210578 2.90091078942173 30 114.6 106.832656114715 7.76734388528549 31 85.4 101.506797047074 -16.1067970470737 32 100.5 100.508198471891 -0.00819847189099976 33 114.8 100.674631567755 14.1253684322452 34 116.5 103.171128005711 13.3288719942886 35 112.9 105.001892060213 7.89810793978704 36 102 106.166923731259 -4.1669237312594 37 106 106.000490635396 -0.000490635395621775 38 105.3 106.999089210578 -1.69908921057828 39 118.8 107.997687785761 10.8023122142391 40 106.1 108.496987073352 -2.39698707335227 41 109.3 109.662018744399 -0.362018744398707 42 117.2 109.994884936126 7.20511506387375 43 92.5 104.835458964349 -12.3354589643492 44 104.2 103.836860389167 0.363139610833475 45 112.5 104.835458964349 7.66454103565081 46 122.4 106.333356827123 16.0666431728768 47 113.3 107.831254689897 5.46874531010283 48 100 107.997687785761 -7.99768778576094 49 110.7 107.997687785761 2.70231221423906 50 112.8 108.663420169216 4.13657983078395 51 109.8 109.662018744399 0.137981255601293 52 117.3 109.994884936126 7.30511506387374 53 109.1 111.492782798900 -2.39278279890025 54 115.9 110.993483511309 4.90651648869109 55 96 106.166923731259 -10.1669237312594 56 99.8 105.501191347804 -5.7011913478043 57 116.8 106.000490635396 10.7995093646044 58 115.7 107.331955402306 8.36804459769417 59 99.4 107.997687785761 -8.59768778576093 60 94.3 107.664821594033 -13.3648215940334 61 91 107.331955402306 -16.3319554023058 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.528051570476999 0.943896859046002 0.471948429523001 6 0.466823046458328 0.933646092916657 0.533176953541671 7 0.358240351662865 0.71648070332573 0.641759648337136 8 0.347555450452192 0.695110900904385 0.652444549547808 9 0.714420192346072 0.571159615307855 0.285579807653928 10 0.713457400981937 0.573085198036126 0.286542599018063 11 0.61944780734921 0.76110438530158 0.38055219265079 12 0.51983788485677 0.96032423028646 0.48016211514323 13 0.505591294960585 0.98881741007883 0.494408705039415 14 0.464907986298014 0.929815972596027 0.535092013701986 15 0.380788049096127 0.761576098192254 0.619211950903873 16 0.300065770105645 0.600131540211291 0.699934229894355 17 0.257635816420091 0.515271632840183 0.742364183579909 18 0.296550878730788 0.593101757461575 0.703449121269212 19 0.631553484162561 0.736893031674877 0.368446515837439 20 0.569662331424583 0.860675337150835 0.430337668575417 21 0.675091403809933 0.649817192380133 0.324908596190067 22 0.62271939177336 0.75456121645328 0.37728060822664 23 0.588562393662596 0.822875212674808 0.411437606337404 24 0.512204212609088 0.975591574781823 0.487795787390912 25 0.458598641358357 0.917197282716714 0.541401358641643 26 0.395692223809445 0.79138444761889 0.604307776190555 27 0.43619894314235 0.8723978862847 0.56380105685765 28 0.3859250400211 0.7718500800422 0.6140749599789 29 0.33246101571173 0.66492203142346 0.66753898428827 30 0.329298229773633 0.658596459547267 0.670701770226367 31 0.531489986059826 0.937020027880347 0.468510013940174 32 0.468571375975014 0.937142751950028 0.531428624024986 33 0.544037371612234 0.911925256775533 0.455962628387766 34 0.640286074213707 0.719427851572585 0.359713925786293 35 0.63899539678888 0.72200920642224 0.36100460321112 36 0.576107786458199 0.847784427083602 0.423892213541801 37 0.499318254239773 0.998636508479547 0.500681745760227 38 0.423187724776112 0.846375449552224 0.576812275223888 39 0.465259130857852 0.930518261715705 0.534740869142148 40 0.39255213768571 0.78510427537142 0.60744786231429 41 0.318463496259847 0.636926992519694 0.681536503740153 42 0.287453040865467 0.574906081730935 0.712546959134533 43 0.344840222845232 0.689680445690463 0.655159777154768 44 0.270653748739594 0.541307497479187 0.729346251260406 45 0.253837884514382 0.507675769028764 0.746162115485618 46 0.488048029076324 0.976096058152649 0.511951970923676 47 0.453590661099389 0.907181322198778 0.546409338900611 48 0.414316961449816 0.828633922899631 0.585683038550184 49 0.341082005422626 0.682164010845253 0.658917994577374 50 0.281369233171101 0.562738466342202 0.718630766828899 51 0.200646686962632 0.401293373925265 0.799353313037368 52 0.182107899795490 0.364215799590979 0.81789210020451 53 0.118530619564024 0.237061239128048 0.881469380435976 54 0.132749402310207 0.265498804620413 0.867250597689793 55 0.119680383794207 0.239360767588413 0.880319616205793 56 0.180728217524365 0.361456435048731 0.819271782475635 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 = 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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