*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: Fri, 20 Nov 2009 09:39:56 -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/Nov/20/t1258735245hwr9j2ezn4m2cgr.htm/, Retrieved Fri, 20 Nov 2009 17:40:57 +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/Nov/20/t1258735245hwr9j2ezn4m2cgr.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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8 5560 8.1 3922 7.7 3759 7.5 4138 7.6 4634 7.8 3996 7.8 4308 7.8 4143 7.5 4429 7.5 5219 7.1 4929 7.5 5755 7.5 5592 7.6 4163 7.7 4962 7.7 5208 7.9 4755 8.1 4491 8.2 5732 8.2 5731 8.2 5040 7.9 6102 7.3 4904 6.9 5369 6.7 5578 6.7 4619 6.9 4731 7 5011 7.1 5299 7.2 4146 7.1 4625 6.9 4736 7 4219 6.8 5116 6.4 4205 6.7 4121 6.6 5103 6.4 4300 6.3 4578 6.2 3809 6.5 5526 6.8 4247 6.8 3830 6.4 4394 6.1 4826 5.8 4409 6.1 4569 7.2 4106 7.3 4794 6.9 3914 6.1 3793 5.8 4405 6.2 4022 7.1 4100 7.7 4788 7.9 3163 7.7 3585 7.4 3903 7.5 4178 8 3863 8.1 4187

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 WerklM[t] = + 6.57206060903754 + 0.000134474457599655Bouwv[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) 6.57206060903754 0.623993 10.5323 0 0 Bouwv 0.000134474457599655 0.000135 0.9972 0.322756 0.161378 Multiple Linear Regression - Regression Statistics Multiple R 0.128739653614468 R-squared 0.0165738984127731 Adjusted R-squared -9.43405971798317e-05 F-TEST (value) 0.994340098127727 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.322756139750018 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.661619789894276 Sum Squared Residuals 25.8267040364050 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8 7.31973859329161 0.680261406708391 2 8.1 7.09946943174339 1.00053056825661 3 7.7 7.07755009515465 0.622449904845355 4 7.5 7.12851591458491 0.371484085415085 5 7.6 7.19521524555434 0.404784754445656 6 7.8 7.10942054160576 0.690579458394236 7 7.8 7.15137657237686 0.648623427623144 8 7.8 7.12918828687291 0.670811713127087 9 7.5 7.16764798174641 0.332352018253586 10 7.5 7.27388280325014 0.226117196749858 11 7.1 7.23488521054624 -0.134885210546242 12 7.5 7.34596111252356 0.154038887476443 13 7.5 7.32404177593481 0.175958224065187 14 7.6 7.13187777602491 0.468122223975094 15 7.7 7.23932286764703 0.46067713235297 16 7.7 7.27240358421655 0.427596415783455 17 7.9 7.2114866549239 0.688513345076099 18 8.1 7.17598539811759 0.924014601882407 19 8.2 7.34286819999877 0.857131800001234 20 8.2 7.34273372554116 0.857266274458834 21 8.2 7.2498118753398 0.950188124660196 22 7.9 7.39262374931064 0.507376250689363 23 7.3 7.23152334910625 0.0684766508937493 24 6.9 7.29405397189009 -0.39405397189009 25 6.7 7.32215913352842 -0.622159133528418 26 6.7 7.19319812869035 -0.493198128690349 27 6.9 7.20825926794151 -0.30825926794151 28 7 7.24591211606941 -0.245912116069414 29 7.1 7.28464075985811 -0.184640759858115 30 7.2 7.12959171024571 0.0704082897542881 31 7.1 7.19400497543595 -0.0940049754359471 32 6.9 7.20893164022951 -0.308931640229508 33 7 7.13940834565049 -0.139408345650487 34 6.8 7.26003193411738 -0.460031934117378 35 6.4 7.13752570324409 -0.737525703244091 36 6.7 7.12622984880572 -0.426229848805720 37 6.6 7.25828376616858 -0.658283766168582 38 6.4 7.15030077671606 -0.750300776716058 39 6.3 7.18768467592876 -0.887684675928763 40 6.2 7.08427381803463 -0.884273818034628 41 6.5 7.31516646173324 -0.815166461733236 42 6.8 7.14317363046328 -0.343173630463277 43 6.8 7.08709778164422 -0.287097781644221 44 6.4 7.16294137573043 -0.762941375730426 45 6.1 7.22103434141348 -1.12103434141348 46 5.8 7.16495849259442 -1.36495849259442 47 6.1 7.18647440581037 -1.08647440581037 48 7.2 7.12421273194173 0.0757872680582743 49 7.3 7.21673115877029 0.0832688412297114 50 6.9 7.09839363608259 -0.198393636082592 51 6.1 7.08212222671303 -0.982122226713034 52 5.8 7.16442059476402 -1.36442059476402 53 6.2 7.11291687750335 -0.912916877503355 54 7.1 7.12340588519613 -0.0234058851961283 55 7.7 7.21592431202469 0.48407568797531 56 7.9 6.99740331842525 0.90259668157475 57 7.7 7.0541515395323 0.645848460467695 58 7.4 7.096914417049 0.303085582951005 59 7.5 7.1338948928889 0.366105107111099 60 8 7.09153543874501 0.90846456125499 61 8.1 7.1351051630073 0.964894836992702 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0992985563781404 0.198597112756281 0.90070144362186 6 0.0365741644446374 0.0731483288892749 0.963425835555363 7 0.0122889515833670 0.0245779031667340 0.987711048416633 8 0.00393779809424459 0.00787559618848917 0.996062201905755 9 0.00262857078960489 0.00525714157920978 0.997371429210395 10 0.00151660733527982 0.00303321467055964 0.99848339266472 11 0.00469525550088094 0.00939051100176188 0.99530474449912 12 0.00180324670690636 0.00360649341381272 0.998196753293094 13 0.000663053966429846 0.00132610793285969 0.99933694603357 14 0.000269159069956744 0.000538318139913488 0.999730840930043 15 0.000104825036840364 0.000209650073680727 0.99989517496316 16 4.0829271095561e-05 8.1658542191122e-05 0.999959170728904 17 2.73893461295734e-05 5.47786922591467e-05 0.99997261065387 18 4.78795769907238e-05 9.57591539814476e-05 0.99995212042301 19 0.000186912391436496 0.000373824782872992 0.999813087608564 20 0.000407078487962548 0.000814156975925097 0.999592921512037 21 0.000904548294511586 0.00180909658902317 0.999095451705488 22 0.000974942902552818 0.00194988580510564 0.999025057097447 23 0.0012698258616924 0.0025396517233848 0.998730174138308 24 0.0058413972284001 0.0116827944568002 0.9941586027716 25 0.0225717111242925 0.045143422248585 0.977428288875708 26 0.0500202717633597 0.100040543526719 0.94997972823664 27 0.0589444423878968 0.117888884775794 0.941055557612103 28 0.0591412239598288 0.118282447919658 0.940858776040171 29 0.0575320608049005 0.115064121609801 0.9424679391951 30 0.0463468345620348 0.0926936691240696 0.953653165437965 31 0.0403940242485457 0.0807880484970915 0.959605975751454 32 0.0398234829307266 0.0796469658614531 0.960176517069273 33 0.0332437194441375 0.066487438888275 0.966756280555862 34 0.0353836839938641 0.0707673679877282 0.964616316006136 35 0.0577642259629707 0.115528451925941 0.94223577403703 36 0.053864837407543 0.107729674815086 0.946135162592457 37 0.0568254381144859 0.113650876228972 0.943174561885514 38 0.067731939082702 0.135463878165404 0.932268060917298 39 0.0830536811178221 0.166107362235644 0.916946318882178 40 0.124014820596055 0.24802964119211 0.875985179403945 41 0.127892186498827 0.255784372997655 0.872107813501173 42 0.0962910189708013 0.192582037941603 0.9037089810292 43 0.0737774602588079 0.147554920517616 0.926222539741192 44 0.0682283613617816 0.136456722723563 0.931771638638218 45 0.0804524378636491 0.160904875727298 0.91954756213635 46 0.16731928662538 0.33463857325076 0.83268071337462 47 0.218428111951902 0.436856223903805 0.781571888048098 48 0.157374999054148 0.314749998108296 0.842625000945852 49 0.113987461030471 0.227974922060943 0.886012538969529 50 0.0794978615051545 0.158995723010309 0.920502138494846 51 0.165351814175123 0.330703628350246 0.834648185824877 52 0.502742091710185 0.99451581657963 0.497257908289815 53 0.934680372643483 0.130639254713033 0.0653196273565167 54 0.965415815492845 0.0691683690143099 0.0345841845071549 55 0.91582935029428 0.16834129941144 0.08417064970572 56 0.835092388416604 0.329815223166792 0.164907611583396 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.307692307692308 NOK 5% type I error level 19 0.365384615384615 NOK 10% type I error level 26 0.5 NOK

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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