paper

*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, 22 Dec 2008 16:26:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/23/t12299923384zsjre8j2jp5ysa.htm/, Retrieved Tue, 23 Dec 2008 01:32:29 +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/2008/Dec/23/t12299923384zsjre8j2jp5ysa.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 0 610763 0 612613 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 560576 0 548854 0 531673 0 525919 0 511038 0 498662 0 555362 0 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1 506174 1 501866 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 Werkloosheid[t] = + 607102.02384106 -60547.5405629139Kredietcrisis[t] -22451.0315397349M1[t] -21083.2324503312M2[t] -19657.5600165564M3[t] -24743.2875827814M4[t] -34927.0151490066M5[t] -41895.1427152318M6[t] -51461.2702814569M7[t] -50342.5978476821M8[t] + 1374.67458609271M9[t] + 23086.4551324503M10[t] + 14821.1275662252M11[t] -389.472433774837t + 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) 607102.02384106 10870.396373 55.8491 0 0 Kredietcrisis -60547.5405629139 9315.917037 -6.4994 0 0 M1 -22451.0315397349 12303.479968 -1.8248 0.074395 0.037198 M2 -21083.2324503312 12911.247205 -1.6329 0.109165 0.054583 M3 -19657.5600165564 12897.303127 -1.5242 0.13417 0.067085 M4 -24743.2875827814 12887.501508 -1.9199 0.060946 0.030473 M5 -34927.0151490066 12881.851804 -2.7113 0.009329 0.004665 M6 -41895.1427152318 12880.359477 -3.2526 0.00212 0.00106 M7 -51461.2702814569 12883.025972 -3.9945 0.000227 0.000113 M8 -50342.5978476821 12889.848709 -3.9056 0.000299 0.00015 M9 1374.67458609271 12900.821093 0.1066 0.915594 0.457797 M10 23086.4551324503 12832.218695 1.7991 0.078425 0.039213 M11 14821.1275662252 12825.954983 1.1556 0.253703 0.126852 t -389.472433774837 231.45582 -1.6827 0.099064 0.049532 Multiple Linear Regression - Regression Statistics Multiple R 0.900632572216153 R-squared 0.811139030136684 Adjusted R-squared 0.758900889536192 F-TEST (value) 15.5277163546102 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 7.93143328792212e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20276.3131165098 Sum Squared Residuals 19323057059.1411 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 547344 584261.519867549 -36917.5198675488 2 554788 585239.846523179 -30451.8465231788 3 562325 586276.046523179 -23951.0465231789 4 560854 580800.846523179 -19946.8465231789 5 555332 570227.646523179 -14895.6465231788 6 543599 562870.046523179 -19271.0465231789 7 536662 552914.446523179 -16252.4465231788 8 542722 553643.646523179 -10921.6465231789 9 593530 604971.446523179 -11441.4465231789 10 610763 626293.754635762 -15530.7546357616 11 612613 617638.954635762 -5025.95463576164 12 611324 602428.354635762 8895.64536423834 13 594167 579587.850662252 14579.1493377481 14 595454 580566.177317881 14887.8226821192 15 590865 581602.377317881 9262.6226821192 16 589379 576127.177317881 13251.8226821192 17 584428 565553.977317881 18874.0226821192 18 573100 558196.377317881 14903.6226821192 19 567456 548240.777317881 19215.2226821192 20 569028 548969.977317881 20058.0226821192 21 620735 600297.777317881 20437.2226821192 22 628884 621620.085430464 7263.91456953642 23 628232 612965.285430464 15266.7145695364 24 612117 597754.685430464 14362.3145695364 25 595404 574914.181456954 20489.8185430462 26 597141 575892.508112583 21248.4918874172 27 593408 576928.708112583 16479.2918874172 28 590072 571453.508112583 18618.4918874172 29 579799 560880.308112583 18918.6918874172 30 574205 553522.708112583 20682.2918874172 31 572775 543567.108112583 29207.8918874172 32 572942 544296.308112583 28645.6918874172 33 619567 595624.108112583 23942.8918874172 34 625809 616946.416225165 8862.58377483447 35 619916 608291.616225166 11624.3837748345 36 587625 593081.016225166 -5456.01622516555 37 565742 570240.512251656 -4498.51225165578 38 557274 571218.838907285 -13944.8389072847 39 560576 572255.038907285 -11679.0389072847 40 548854 566779.838907285 -17925.8389072847 41 531673 556206.638907285 -24533.6389072847 42 525919 548849.038907285 -22930.0389072847 43 511038 538893.438907285 -27855.4389072847 44 498662 539622.638907285 -40960.6389072847 45 555362 590950.438907285 -35588.4389072847 46 564591 551725.206456954 12865.7935430464 47 541657 543070.406456954 -1413.40645695364 48 527070 527859.806456954 -789.806456953648 49 509846 505019.302483444 4826.69751655612 50 514258 505997.629139073 8260.3708609272 51 516922 507033.829139073 9888.1708609272 52 507561 501558.629139073 6002.37086092718 53 492622 490985.429139073 1636.57086092717 54 490243 483627.829139073 6615.17086092718 55 469357 473672.229139073 -4315.22913907285 56 477580 474401.429139073 3178.57086092715 57 528379 525729.229139073 2649.77086092719 58 533590 547051.537251656 -13461.5372516556 59 517945 538396.737251656 -20451.7372516556 60 506174 523186.137251656 -17012.1372516556 61 501866 500345.633278146 1520.36672185417 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.183236378449972 0.366472756899944 0.816763621550028 18 0.101401117423682 0.202802234847364 0.898598882576318 19 0.0495380338578638 0.0990760677157276 0.950461966142136 20 0.0306431939569822 0.0612863879139644 0.969356806043018 21 0.0181935881913819 0.0363871763827638 0.981806411808618 22 0.034346454497868 0.068692908995736 0.965653545502132 23 0.0483400779965989 0.0966801559931978 0.951659922003401 24 0.198353991656342 0.396707983312684 0.801646008343658 25 0.2254037855854 0.4508075711708 0.7745962144146 26 0.217354277875766 0.434708555751531 0.782645722124234 27 0.243889494773458 0.487778989546916 0.756110505226542 28 0.244232660885381 0.488465321770762 0.755767339114619 29 0.262699360186525 0.525398720373050 0.737300639813475 30 0.215253405386046 0.430506810772092 0.784746594613954 31 0.201626368796947 0.403252737593893 0.798373631203053 32 0.251533776735327 0.503067553470654 0.748466223264673 33 0.32346847995041 0.64693695990082 0.67653152004959 34 0.396604154207428 0.793208308414856 0.603395845792572 35 0.874315613071907 0.251368773856186 0.125684386928093 36 0.989004802894518 0.0219903942109647 0.0109951971054823 37 0.995574006290989 0.00885198741802185 0.00442599370901093 38 0.996739796858882 0.00652040628223685 0.00326020314111843 39 0.996348689040763 0.00730262191847347 0.00365131095923674 40 0.99542690713713 0.00914618572574024 0.00457309286287012 41 0.993467365865486 0.0130652682690275 0.00653263413451375 42 0.985947317603785 0.0281053647924304 0.0140526823962152 43 0.987482733000622 0.0250345339987563 0.0125172669993782 44 0.966226690107214 0.0675466197855712 0.0337733098927856 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.142857142857143 NOK 5% type I error level 9 0.321428571428571 NOK 10% type I error level 14 0.5 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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