Verbetering WS10

*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: Mon, 20 Dec 2010 08:24:20 +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/20/t1292833344v65227njnxe0wow.htm/, Retrieved Mon, 20 Dec 2010 09:22:27 +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/20/t1292833344v65227njnxe0wow.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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No (this computation is public)

User-defined keywords:

Dataseries X:

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0.504208603 0.397232704 0.457969746 0.382767296 0.509923035 0.396037736 0.606622221 0.441761006 0.626210885 0.445220126 0.626631316 0.438490566 0.676731276 0.467484277 0.613117455 0.465786164 0.486215861 0.402075472 0.452529881 0.376163522 0.467150592 0.37591195 0.494624486 0.392955975 0.444567428 0.34490566 0.478862605 0.368553459 0.544458459 0.390880503 0.628201498 0.424842767 0.672578445 0.426855346 0.652706633 0.442327044 0.645430599 0.474842767 0.576334011 0.447610063 0.618334234 0.480754717 0.639896351 0.516037736 0.72850438 0.580628931 0.694655375 0.573522013 0.689773225 0.578867925 0.712244845 0.593584906 0.760337031 0.645974843 0.837816503 0.690503145 0.90688735 0.782201258 0.976018259 0.839056604 0.962066806 0.847484277 0.837593417 0.726855346 0.767638807 0.635534591 0.580006349 0.470943396 0.387740568 0.346163522 0.331274078 0.272327044 0.345251272 0.286792453 0.380172806 0.27672956 0.399838692 0.297421384 0.425742404 0.321698113 0.524183377 0.365597484 0.59 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation olie[t] = -0.0821808528703387 + 0.945106889984705benzine[t] -0.00109177410960875M1[t] -0.00524818743131263M2[t] -0.0216078434842863M3[t] -0.0479609090217005M4[t] -0.0691464777635879M5[t] -0.058274475041758M6[t] -0.0424983401680099M7[t] -0.0303160965189834M8[t] -0.0163841445707708M9[t] -0.0094090313816478M10[t] -0.00436586437226947M11[t] + 0.00048529461501224t + 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) -0.0821808528703387 0.022579 -3.6397 0.000701 0.000351 benzine 0.945106889984705 0.031207 30.2856 0 0 M1 -0.00109177410960875 0.019339 -0.0565 0.955229 0.477614 M2 -0.00524818743131263 0.019327 -0.2715 0.78721 0.393605 M3 -0.0216078434842863 0.019369 -1.1156 0.270508 0.135254 M4 -0.0479609090217005 0.019621 -2.4444 0.01849 0.009245 M5 -0.0691464777635879 0.019874 -3.4792 0.001128 0.000564 M6 -0.058274475041758 0.019983 -2.9163 0.005507 0.002753 M7 -0.0424983401680099 0.019923 -2.1331 0.038403 0.019202 M8 -0.0303160965189834 0.0197 -1.5389 0.130831 0.065415 M9 -0.0163841445707708 0.019471 -0.8415 0.404544 0.202272 M10 -0.0094090313816478 0.019393 -0.4852 0.629904 0.314952 M11 -0.00436586437226947 0.019381 -0.2253 0.822791 0.411395 t 0.00048529461501224 0.000224 2.1676 0.035522 0.017761 Multiple Linear Regression - Regression Statistics Multiple R 0.978985184238817 R-squared 0.958411990959111 Adjusted R-squared 0.946397677236188 F-TEST (value) 79.7725124432574 F-TEST (DF numerator) 13 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0287798049466305 Sum Squared Residuals 0.0372724727744743 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.397232704 0.393743692319928 0.00348901168007235 2 0.382767296 0.346371911277518 0.0363953847224817 3 0.396037736 0.379598961230824 0.0164387747691764 4 0.441761006 0.445122257252934 -0.003361251252934 5 0.445220126 0.442935364438054 0.00228476156194571 6 0.438490566 0.45469001400976 -0.0161994480097595 7 0.467484277 0.518301260882478 -0.0508169838824781 8 0.465786164 0.470846938621163 -0.00506077462116303 9 0.402075472 0.365328614344946 0.0367468576550537 10 0.376163522 0.340952170355194 0.0352113516448055 11 0.37591195 0.36029876668216 0.0156131833178398 12 0.392955975 0.391115692183551 0.00184028281644867 13 0.34490566 0.343199942280791 0.00170571771920913 14 0.368553459 0.371941431650044 -0.00338797265004419 15 0.390880503 0.418062163781914 -0.0271816607819135 16 0.424842767 0.471340516006669 -0.0464977490066694 17 0.426855346 0.49258120024598 -0.0657258542459803 18 0.442327044 0.485157511145142 -0.0428304671451417 19 0.474842767 0.494542310768739 -0.0196995437687391 20 0.447610063 0.441906187639543 0.00570387536045662 21 0.480754717 0.496018134340962 -0.0152634173409623 22 0.516037736 0.523857047484454 -0.00781931148445382 23 0.580628931 0.613129567824709 -0.0325006368247089 24 0.573522013 0.585989798967364 -0.0124677859673639 25 0.578867925 0.580769165869829 -0.00190124086982872 26 0.593584906 0.598336130054255 -0.004751224054255 27 0.645974843 0.62791402495932 0.0180608180406804 28 0.690503145 0.675272636856495 0.0152305081435054 29 0.782201258 0.719851696126399 0.0623495618736011 30 0.839056604 0.796545091870047 0.0425115121299535 31 0.847484277 0.799620907003209 0.0478633699967908 32 0.726855346 0.694647787703602 0.0322075582963985 33 0.635534591 0.642950450369633 -0.00741585936963354 34 0.470943396 0.473078129333203 -0.002134733333203 35 0.346163522 0.296894876626203 0.0492686453737968 36 0.272327044 0.248379166861232 0.0239478771387676 37 0.286792453 0.260982629718689 0.0258098232813112 38 0.27672956 0.290316093404232 -0.0135865334042323 39 0.297421384 0.293028096322525 0.00439328767747539 40 0.321698113 0.291642102087502 0.0300560109124979 41 0.365597484 0.363979069799725 0.00161841420027471 42 0.435220126 0.444264855581587 -0.00904472958158742 43 0.412893082 0.407954120787822 0.00493896121217841 44 0.458679245 0.490134012796054 -0.0314547677960544 45 0.428427673 0.441120831955629 -0.0126931589556288 46 0.463522013 0.473736082824808 -0.0102140698248081 47 0.487169811 0.506576444663744 -0.0194066336637442 48 0.473584906 0.486905279987852 -0.0133203739878523 49 0.491886792 0.520990103810764 -0.0291033118107639 50 0.474842767 0.48951242161395 -0.0146696546139501 51 0.502327044 0.514038263705419 -0.0117112197054186 52 0.539371069 0.5347985877964 0.00457248120360015 53 0.484402516 0.484929399389841 -0.000526883389841208 54 0.474654088 0.449090955393465 0.0255631326065351 55 0.473522013 0.455807816557752 0.017714196442248 56 0.48754717 0.488943061239638 -0.00139589123963766 57 0.493333333 0.494707754988829 -0.00137442198882909 58 0.525157233 0.54020047000234 -0.0150432370023405 59 0.542704403 0.555678961203183 -0.0129745582031835 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0137611498542259 0.0275222997084518 0.986238850145774 18 0.0235701293376089 0.0471402586752178 0.976429870662391 19 0.139579244264716 0.279158488529432 0.860420755735284 20 0.072768228748172 0.145536457496344 0.927231771251828 21 0.163658304292435 0.327316608584871 0.836341695707565 22 0.223384534326035 0.44676906865207 0.776615465673965 23 0.325849620998019 0.651699241996037 0.674150379001981 24 0.413924610766697 0.827849221533394 0.586075389233303 25 0.563297020143388 0.873405959713224 0.436702979856612 26 0.507294597902798 0.985410804194403 0.492705402097202 27 0.651098076898052 0.697803846203897 0.348901923101948 28 0.791321222547845 0.417357554904311 0.208678777452155 29 0.964600223888363 0.0707995522232743 0.0353997761116371 30 0.965853139000405 0.0682937219991901 0.034146860999595 31 0.976223379587537 0.0475532408249269 0.0237766204124635 32 0.99559291234919 0.00881417530162048 0.00440708765081024 33 0.99797232355601 0.00405535288797909 0.00202767644398954 34 0.99826724757383 0.00346550485233967 0.00173275242616984 35 0.999979918062671 4.0163874657696e-05 2.0081937328848e-05 36 0.999929782277216 0.000140435445567633 7.02177227838166e-05 37 0.999974258647476 5.1482705047426e-05 2.5741352523713e-05 38 0.999960807024096 7.83859518072013e-05 3.91929759036007e-05 39 0.999830157512965 0.000339684974069843 0.000169842487034921 40 0.999586302388342 0.000827395223315066 0.000413697611657533 41 0.999757876681805 0.000484246636390009 0.000242123318195004 42 0.998245210101208 0.0035095797975837 0.00175478989879185 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.423076923076923 NOK 5% type I error level 14 0.538461538461538 NOK 10% type I error level 16 0.615384615384615 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = 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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