*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, 14 Dec 2009 02:40:28 -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/14/t12607837050vozmuxzmndgqv5.htm/, Retrieved Mon, 14 Dec 2009 10:41:57 +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/Dec/14/t12607837050vozmuxzmndgqv5.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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95.1 121.8 97.0 127.6 112.7 129.9 102.9 128.0 97.4 123.5 111.4 124.0 87.4 127.4 96.8 127.6 114.1 128.4 110.3 131.4 103.9 135.1 101.6 134.0 94.6 144.5 95.9 147.3 104.7 150.9 102.8 148.7 98.1 141.4 113.9 138.9 80.9 139.8 95.7 145.6 113.2 147.9 105.9 148.5 108.8 151.1 102.3 157.5 99.0 167.5 100.7 172.3 115.5 173.5 100.7 187.5 109.9 205.5 114.6 195.1 85.4 204.5 100.5 204.5 114.8 201.7 116.5 207.0 112.9 206.6 102.0 210.6 106.0 211.1 105.3 215.0 118.8 223.9 106.1 238.2 109.3 238.9 117.2 229.6 92.5 232.2 104.2 222.1 112.5 221.6 122.4 227.3 113.3 221.0 100.0 213.6 110.7 243.4 112.8 253.8 109.8 265.3 117.3 268.2 109.1 268.5 115.9 266.9 96.0 268.4 99.8 250.8 116.8 231.2 115.7 192.0 99.4 171.4 94.3 160.0

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TIP[t] = + 92.2540176785407 + 0.0707030335485437Grondstofprijzen[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) 92.2540176785407 4.501318 20.4949 0 0 Grondstofprijzen 0.0707030335485437 0.023457 3.0142 0.003817 0.001909 Multiple Linear Regression - Regression Statistics Multiple R 0.368007133872716 R-squared 0.135429250581211 Adjusted R-squared 0.120522858349853 F-TEST (value) 9.08531376870052 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00381734138297962 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.43994827471276 Sum Squared Residuals 4131.49815902996 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 100.865647164753 -5.76564716475336 2 97 101.275724759335 -4.27572475933489 3 112.7 101.438341736497 11.2616582635034 4 102.9 101.304005972754 1.59599402724568 5 97.4 100.985842321786 -3.58584232178587 6 111.4 101.021193838560 10.3788061614399 7 87.4 101.261584152625 -13.8615841526252 8 96.8 101.275724759335 -4.47572475933491 9 114.1 101.332287186174 12.7677128138263 10 110.3 101.544396286819 8.75560371318062 11 103.9 101.805997510949 2.09400248905102 12 101.6 101.728224174046 -0.128224174045595 13 94.6 102.470606026305 -7.8706060263053 14 95.9 102.668574520241 -6.76857452024122 15 104.7 102.923105441016 1.77689455898402 16 102.8 102.767558767209 0.0324412327908161 17 98.1 102.251426622305 -4.15142662230482 18 113.9 102.074669038433 11.8253309615666 19 80.9 102.138301768627 -21.2383017686271 20 95.7 102.548379363209 -6.8483793632087 21 113.2 102.710996340370 10.4890036596297 22 105.9 102.753418160499 3.14658183950053 23 108.8 102.937246047726 5.86275395227431 24 102.3 103.389745462436 -1.08974546243637 25 99 104.096775797922 -5.0967757979218 26 100.7 104.436150358955 -3.73615035895481 27 115.5 104.520993999213 10.9790060007869 28 100.7 105.510836468893 -4.81083646889268 29 109.9 106.783491072766 3.11650892723354 30 114.6 106.048179523862 8.55182047613838 31 85.4 106.712788039218 -21.3127880392179 32 100.5 106.712788039218 -6.21278803921792 33 114.8 106.514819545282 8.285180454718 34 116.5 106.889545623089 9.61045437691072 35 112.9 106.861264409670 6.03873559033014 36 102 107.144076543864 -5.14407654386404 37 106 107.179428060638 -1.17942806063831 38 105.3 107.455169891478 -2.15516989147763 39 118.8 108.084426890060 10.7155731099403 40 106.1 109.095480269804 -2.99548026980385 41 109.3 109.144972393288 0.15502760671217 42 117.2 108.487434181286 8.71256581871364 43 92.5 108.671262068513 -16.1712620685126 44 104.2 107.957161429672 -3.75716142967229 45 112.5 107.921809912898 4.57819008710198 46 122.4 108.324817204125 14.0751827958753 47 113.3 107.879388092769 5.4206119072311 48 100 107.356185644510 -7.35618564450967 49 110.7 109.463136044256 1.23686395574373 50 112.8 110.198447593161 2.60155240683887 51 109.8 111.011532478969 -1.21153247896938 52 117.3 111.216571276260 6.08342872373984 53 109.1 111.237782186325 -2.13778218632473 54 115.9 111.124657332647 4.77534266735296 55 96 111.230711882970 -15.2307118829699 56 99.8 109.986338492516 -10.1863384925155 57 116.8 108.600559034964 8.19944096503596 58 115.7 105.829000119861 9.87099988013888 59 99.4 104.372517628761 -4.97251762876112 60 94.3 103.566503046308 -9.26650304630773 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.200197057706074 0.400394115412148 0.799802942293926 6 0.448529141787076 0.897058283574152 0.551470858212924 7 0.72813091848563 0.54373816302874 0.27186908151437 8 0.64075520720967 0.71848958558066 0.35924479279033 9 0.71159849420974 0.576803011580521 0.288401505790260 10 0.63625223340834 0.72749553318332 0.36374776659166 11 0.577115980097850 0.845768039804301 0.422884019902150 12 0.503024206303266 0.993951587393469 0.496975793696734 13 0.540969061996276 0.918061876007447 0.459030938003724 14 0.471109412769617 0.942218825539234 0.528890587230383 15 0.405512527752595 0.811025055505191 0.594487472247405 16 0.322204874525279 0.644409749050558 0.677795125474721 17 0.258100583563407 0.516201167126814 0.741899416436593 18 0.341967568752801 0.683935137505601 0.658032431247199 19 0.721520017364041 0.556959965271917 0.278479982635958 20 0.684009561486723 0.631980877026555 0.315990438513278 21 0.735936487624036 0.528127024751928 0.264063512375964 22 0.679742202639138 0.640515594721724 0.320257797360862 23 0.643004584892199 0.713990830215602 0.356995415107801 24 0.568149034689573 0.863701930620855 0.431850965310427 25 0.511450910931146 0.977098178137708 0.488549089068854 26 0.443808705711239 0.887617411422479 0.55619129428876 27 0.500440186210443 0.999119627579113 0.499559813789557 28 0.445580296931844 0.891160593863688 0.554419703068156 29 0.382160933037142 0.764321866074284 0.617839066962858 30 0.373915725437514 0.747831450875028 0.626084274562486 31 0.735575757578192 0.528848484843617 0.264424242421808 32 0.699494771039306 0.601010457921389 0.300505228960694 33 0.705589556993098 0.588820886013804 0.294410443006902 34 0.726670177277462 0.546659645445077 0.273329822722538 35 0.693889898573915 0.612220202852169 0.306110101426085 36 0.647332302151539 0.705335395696922 0.352667697848461 37 0.572499712012438 0.855000575975124 0.427500287987562 38 0.497695188095014 0.995390376190028 0.502304811904986 39 0.540931369273645 0.91813726145271 0.459068630726355 40 0.469588335196545 0.93917667039309 0.530411664803455 41 0.388595700687334 0.777191401374669 0.611404299312666 42 0.389975300402987 0.779950600805974 0.610024699597013 43 0.595959465717844 0.808081068564311 0.404040534282156 44 0.525622692622378 0.948754614755244 0.474377307377622 45 0.460091610056465 0.92018322011293 0.539908389943535 46 0.625297614120775 0.74940477175845 0.374702385879225 47 0.585401794690181 0.829196410619638 0.414598205309819 48 0.540038286898997 0.919923426202005 0.459961713101003 49 0.441400441482718 0.882800882965435 0.558599558517282 50 0.352913993599701 0.705827987199401 0.647086006400299 51 0.255864479465204 0.511728958930409 0.744135520534796 52 0.226901318934835 0.453802637869670 0.773098681065165 53 0.145470731393108 0.290941462786216 0.854529268606892 54 0.134538196775102 0.269076393550205 0.865461803224898 55 0.173674063916561 0.347348127833121 0.82632593608344 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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