*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: Thu, 02 Dec 2010 23:08:46 +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/03/t12913312504seady1kg5o46w4.htm/, Retrieved Fri, 03 Dec 2010 00:07:30 +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/03/t12913312504seady1kg5o46w4.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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2.172 286602 2.150 283042 2.533 276687 2.058 277915 2.160 277128 2.260 277103 2.498 275037 2.695 270150 2.799 267140 2.947 264993 2.930 287259 2.318 291186 2.540 292300 2.570 288186 2.669 281477 2.450 282656 2.842 280190 3.440 280408 2.678 276836 2.981 275216 2.260 274352 2.844 271311 2.546 289802 2.456 290726 2.295 292300 2.379 278506 2.479 269826 2.057 265861 2.280 269034 2.351 264176 2.276 255198 2.548 253353 2.311 246057 2.201 235372 2.725 258556 2.408 260993 2.139 254663 1.898 250643 2.539 243422 2.069 247105 2.063 248541 2.565 245039 2.442 237080 2.194 237085 2.798 225554 2.074 226839 2.628 247934 2.289 248333 2.154 246969 2.466 245098 2.137 246263 1.846 255765 2.072 264319 1.786 268347 1.754 273046 2.226 273963 1.947 267430 1.823 271993 2.521 292710 2.072 295881 2.368 294563

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Bouw[t] = + 1.59989141489623 + 2.91128188854254e-06NWWM[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) 1.59989141489623 0.623346 2.5666 0.012827 0.006414 NWWM 2.91128188854254e-06 2e-06 1.249 0.216611 0.108305 Multiple Linear Regression - Regression Statistics Multiple R 0.160493568743607 R-squared 0.0257581856080589 Adjusted R-squared 0.00924561248277178 F-TEST (value) 1.55991349213849 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.216610691689592 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.328427337791871 Sum Squared Residuals 6.3640064563343 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.172 2.43427062671630 -0.262270626716297 2 2.15 2.42390646319309 -0.273906463193087 3 2.533 2.4054052667914 0.127594733208601 4 2.058 2.40898032095053 -0.35098032095053 5 2.16 2.40668914210425 -0.246689142104247 6 2.26 2.40661636005703 -0.146616360057033 7 2.498 2.40060165167530 0.097398348324696 8 2.695 2.38637421708600 0.308625782914003 9 2.799 2.37761125860148 0.421388741398516 10 2.947 2.37136073638678 0.575639263613217 11 2.93 2.43618333891707 0.493816661082929 12 2.318 2.44761594289338 -0.129615942893378 13 2.54 2.45085911091721 0.089140889082786 14 2.57 2.43888209722775 0.131117902772250 15 2.669 2.41935030703752 0.249649692962482 16 2.45 2.42278270838411 0.0272172916158904 17 2.842 2.41560348724696 0.426396512753036 18 3.44 2.41623814669867 1.02376185330133 19 2.678 2.40583904779279 0.272160952207208 20 2.981 2.40112277113335 0.579877228866646 21 2.26 2.39860742358165 -0.138607423581653 22 2.844 2.38975421535859 0.454245784641405 23 2.546 2.44358672875963 0.102413271240365 24 2.456 2.44627675322465 0.00972324677535187 25 2.295 2.45085911091721 -0.155859110917214 26 2.379 2.41070088854666 -0.0317008885466583 27 2.479 2.38543096175411 0.093569038245891 28 2.057 2.37388772906604 -0.316887729066038 29 2.28 2.38312522649838 -0.103125226498384 30 2.351 2.36898221908384 -0.0179822190838437 31 2.276 2.34284473028851 -0.066844730288509 32 2.548 2.33747341520415 0.210526584795852 33 2.311 2.31623270254534 -0.00523270254534151 34 2.201 2.28512565556626 -0.0841256555662644 35 2.725 2.35262081487023 0.372379185129765 36 2.408 2.35971560883261 0.0482843911673871 37 2.139 2.34128719447814 -0.202287194478139 38 1.898 2.32958384128620 -0.431583841286198 39 2.539 2.30856147476903 0.230438525230968 40 2.069 2.31928372596453 -0.250283725964534 41 2.063 2.32346432675648 -0.260464326756481 42 2.565 2.31326901758281 0.251730982417195 43 2.442 2.29009812503190 0.151901874968105 44 2.194 2.29011268144134 -0.0961126814413378 45 2.798 2.25654268998455 0.541457310015446 46 2.074 2.26028368721133 -0.186283687211331 47 2.628 2.32169717865014 0.306302821349864 48 2.289 2.32285878012366 -0.0338587801236641 49 2.154 2.31888779162769 -0.164887791627692 50 2.466 2.31344078321423 0.152559216785771 51 2.137 2.31683242661438 -0.179832426614381 52 1.846 2.34449542711931 -0.498495427119312 53 2.072 2.36939853239391 -0.297398532393905 54 1.786 2.38112517584095 -0.595125175840955 55 1.754 2.39480528943522 -0.640805289435216 56 2.226 2.39747493492701 -0.171474934927010 57 1.947 2.37845553034916 -0.431455530349161 58 1.823 2.39173970960658 -0.568739709606581 59 2.521 2.45205273649152 0.0689472635084834 60 2.072 2.46128441136008 -0.389284411360085 61 2.368 2.45744734183099 -0.089447341830986 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.219244649301972 0.438489298603944 0.780755350698028 6 0.102609586905533 0.205219173811066 0.897390413094467 7 0.0696071399422288 0.139214279884458 0.930392860057771 8 0.0478361783469515 0.095672356693903 0.952163821653048 9 0.0262402290183842 0.0524804580367684 0.973759770981616 10 0.0165759944834649 0.0331519889669297 0.983424005516535 11 0.470969503896485 0.94193900779297 0.529030496103515 12 0.383095878965274 0.766191757930548 0.616904121034726 13 0.356855158335535 0.713710316671071 0.643144841664465 14 0.302853995232906 0.605707990465813 0.697146004767094 15 0.261604661627685 0.523209323255369 0.738395338372315 16 0.192071567716268 0.384143135432535 0.807928432283732 17 0.221493104865527 0.442986209731054 0.778506895134473 18 0.831240035665003 0.337519928669994 0.168759964334997 19 0.806106679772393 0.387786640455214 0.193893320227607 20 0.886667198612617 0.226665602774766 0.113332801387383 21 0.879655965217148 0.240688069565703 0.120344034782852 22 0.909289164735625 0.181421670528750 0.0907108352643752 23 0.896881307275836 0.206237385448328 0.103118692724164 24 0.875321474898796 0.249357050202409 0.124678525101205 25 0.841867481193826 0.316265037612347 0.158132518806173 26 0.81659118182819 0.366817636343621 0.183408818171811 27 0.801318242204659 0.397363515590682 0.198681757795341 28 0.852217472734259 0.295565054531482 0.147782527265741 29 0.828826726569057 0.342346546861886 0.171173273430943 30 0.79633736167255 0.407325276654899 0.203662638327450 31 0.758996041023999 0.482007917952001 0.241003958976001 32 0.735539556133055 0.52892088773389 0.264460443866945 33 0.680807674621513 0.638384650756974 0.319192325378487 34 0.628999193754808 0.742001612490384 0.371000806245192 35 0.709713730695912 0.580572538608176 0.290286269304088 36 0.668371334577458 0.663257330845085 0.331628665422542 37 0.625026848544935 0.749946302910129 0.374973151455065 38 0.678564561178579 0.642870877642842 0.321435438821421 39 0.658782567171248 0.682434865657504 0.341217432828752 40 0.621936544215715 0.75612691156857 0.378063455784285 41 0.582865128664314 0.834269742671372 0.417134871335686 42 0.577549761174878 0.844900477650244 0.422450238825122 43 0.519444434135651 0.961111131728699 0.480555565864349 44 0.439766125429903 0.879532250859806 0.560233874570097 45 0.641545980475992 0.716908039048015 0.358454019524008 46 0.572742153801674 0.854515692396652 0.427257846198326 47 0.705323152189898 0.589353695620203 0.294676847810102 48 0.663018179376254 0.673963641247492 0.336981820623746 49 0.590011002885935 0.81997799422813 0.409988997114065 50 0.798365439598129 0.403269120803743 0.201634560401871 51 0.874681248978434 0.250637502043132 0.125318751021566 52 0.83253210169662 0.334935796606761 0.167467898303381 53 0.823124331035016 0.353751337929967 0.176875668964983 54 0.762666464517444 0.474667070965113 0.237333535482556 55 0.763461612966574 0.473076774066852 0.236538387033426 56 0.699881450640564 0.600237098718873 0.300118549359436 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 1 0.0192307692307692 OK 10% type I error level 3 0.0576923076923077 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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