*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 05:20:42 -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/t1258720207b00zj70fvnfzvwx.htm/, Retrieved Fri, 20 Nov 2009 13:30:19 +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/t1258720207b00zj70fvnfzvwx.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:

WS7,MR3

Dataseries X:

» Textbox « » Textfile « » CSV «

1.3 2 1.2 2.1 1.1 2.1 1.4 2.5 1.2 2.2 1.5 2.3 1.1 2.3 1.3 2.2 1.5 2.2 1.1 1.6 1.4 1.8 1.3 1.7 1.5 1.9 1.6 1.8 1.7 1.9 1.1 1.5 1.6 1 1.3 0.8 1.7 1.1 1.6 1.5 1.7 1.7 1.9 2.3 1.8 2.4 1.9 3 1.6 3 1.5 3.2 1.6 3.2 1.6 3.2 1.7 3.5 2 4 2 4.3 1.9 4.1 1.7 4 1.8 4.1 1.9 4.2 1.7 4.5 2 5.6 2.1 6.5 2.4 7.6 2.5 8.5 2.5 8.7 2.6 8.3 2.2 8.3 2.5 8.5 2.8 8.7 2.8 8.7 2.9 8.5 3 7.9 3.1 7 2.9 5.8 2.7 4.5 2.2 3.7 2.5 3.1 2.3 2.7 2.6 2.3 2.3 1.8 2.2 1.5 1.8 1.2 1.8 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation inflatie[t] = + 0.959584165715367 + 0.100154534940552inflatie_levensmiddelen[t] + 0.0190340617400944t + 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) 0.959584165715367 0.062711 15.3017 0 0 inflatie_levensmiddelen 0.100154534940552 0.013508 7.4142 0 0 t 0.0190340617400944 0.001952 9.75 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.915662322330004 R-squared 0.838437488534777 Adjusted R-squared 0.83266739883959 F-TEST (value) 145.307531221605 F-TEST (DF numerator) 2 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.222614569674175 Sum Squared Residuals 2.77520581134822 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.3 1.17892729733656 0.121072702663439 2 1.2 1.20797681257071 -0.00797681257071426 3 1.1 1.22701087431081 -0.127010874310808 4 1.4 1.28610675002712 0.113893249972877 5 1.2 1.27509445128505 -0.0750944512850522 6 1.5 1.30414396651920 0.195856033480798 7 1.1 1.32317802825930 -0.223178028259296 8 1.3 1.33219663650534 -0.0321966365053355 9 1.5 1.35123069824543 0.14876930175457 10 1.1 1.31017203902119 -0.210172039021193 11 1.4 1.34923700774940 0.0507629922506017 12 1.3 1.35825561599544 -0.0582556159954374 13 1.5 1.39732058472364 0.102679415276358 14 1.6 1.40633919296968 0.193660807030319 15 1.7 1.43538870820383 0.264611291796169 16 1.1 1.41436095596770 -0.314360955967705 17 1.6 1.38331775023752 0.216682249762477 18 1.3 1.38232090498951 -0.0823209049895077 19 1.7 1.43140132721177 0.268598672788232 20 1.6 1.49049720292808 0.109502797071918 21 1.7 1.52956217165629 0.170437828343713 22 1.9 1.60868895436071 0.291311045639287 23 1.8 1.63773846959486 0.162261530405138 24 1.9 1.71686525229929 0.183134747700712 25 1.6 1.73589931403938 -0.135899314039382 26 1.5 1.77496428276759 -0.274964282767587 27 1.6 1.79399834450768 -0.193998344507681 28 1.6 1.81303240624778 -0.213032406247776 29 1.7 1.86211282847004 -0.162112828470036 30 2 1.93122415768041 0.0687758423195941 31 2 1.98030457990267 0.0196954200973343 32 1.9 1.97930773465465 -0.07930773465465 33 1.7 1.98832634290069 -0.288326342900689 34 1.8 2.01737585813484 -0.217375858134839 35 1.9 2.04642537336899 -0.146425373368988 36 1.7 2.09550579559125 -0.395505795591248 37 2 2.22470984576595 -0.224709845765949 38 2.1 2.33388298895254 -0.23388298895254 39 2.4 2.46308703912724 -0.0630870391272415 40 2.5 2.57226018231383 -0.0722601823138322 41 2.5 2.61132515104204 -0.111325151042037 42 2.6 2.59029739880591 0.0097026011940892 43 2.2 2.60933146054601 -0.409331460546005 44 2.5 2.64839642927421 -0.14839642927421 45 2.8 2.68746139800241 0.112538601997585 46 2.8 2.70649545974251 0.0935045402574906 47 2.9 2.70549861449449 0.194501385505507 48 3 2.66443995527026 0.335560044729743 49 3.1 2.59333493556385 0.506665064436145 50 2.9 2.49218355537529 0.407816444624713 51 2.7 2.38101672169266 0.318983278307335 52 2.2 2.31992715548032 -0.119927155480318 53 2.5 2.27886849625608 0.221131503743919 54 2.3 2.25784074401996 0.0421592559800446 55 2.6 2.23681299178383 0.363187008216171 56 2.3 2.20576978605365 0.0942302139463522 57 2.2 2.19475748731158 0.00524251268842362 58 1.8 2.18374518856951 -0.383745188569506 59 1.8 2.18274834332149 -0.38274834332149 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.25929306417549 0.51858612835098 0.74070693582451 7 0.242322466874788 0.484644933749577 0.757677533125212 8 0.160258027060674 0.320516054121347 0.839741972939326 9 0.171541430802931 0.343082861605863 0.828458569197069 10 0.105780860271368 0.211561720542735 0.894219139728633 11 0.0854793044867962 0.170958608973592 0.914520695513204 12 0.0477414462325029 0.0954828924650058 0.952258553767497 13 0.0336929873574873 0.0673859747149746 0.966307012642513 14 0.0333157112530174 0.0666314225060348 0.966684288746983 15 0.0328705806565173 0.0657411613130346 0.967129419343483 16 0.0674767473812628 0.134953494762526 0.932523252618737 17 0.111685538938559 0.223371077877118 0.88831446106144 18 0.0750779515437256 0.150155903087451 0.924922048456274 19 0.090807553765976 0.181615107531952 0.909192446234024 20 0.0639879141552076 0.127975828310415 0.936012085844792 21 0.0485583105933667 0.0971166211867334 0.951441689406633 22 0.0495598477379888 0.0991196954759776 0.950440152262011 23 0.0490724072499492 0.0981448144998984 0.95092759275005 24 0.0571349647202054 0.114269929440411 0.942865035279794 25 0.0940045169983884 0.188009033996777 0.905995483001612 26 0.138417405786565 0.27683481157313 0.861582594213435 27 0.121191132309916 0.242382264619831 0.878808867690084 28 0.099999997397911 0.199999994795822 0.900000002602089 29 0.0722428044812449 0.144485608962490 0.927757195518755 30 0.0830096818070654 0.166019363614131 0.916990318192935 31 0.0841165643256958 0.168233128651392 0.915883435674304 32 0.0730364014695299 0.146072802939060 0.92696359853047 33 0.0639237541946296 0.127847508389259 0.936076245805370 34 0.0494944415731385 0.098988883146277 0.950505558426862 35 0.0435185144107959 0.0870370288215918 0.956481485589204 36 0.0380633942046760 0.0761267884093519 0.961936605795324 37 0.0263912830287878 0.0527825660575756 0.973608716971212 38 0.0174392904735185 0.034878580947037 0.982560709526481 39 0.0186579609833672 0.0373159219667344 0.981342039016633 40 0.0146686128188381 0.0293372256376761 0.985331387181162 41 0.00935960989957256 0.0187192197991451 0.990640390100427 42 0.00692999075154457 0.0138599815030891 0.993070009248455 43 0.0254771136451331 0.0509542272902663 0.974522886354867 44 0.087463354215926 0.174926708431852 0.912536645784074 45 0.155032989780642 0.310065979561284 0.844967010219358 46 0.257363384014198 0.514726768028397 0.742636615985802 47 0.325835012138087 0.651670024276175 0.674164987861913 48 0.350651936358433 0.701303872716865 0.649348063641567 49 0.378135879234983 0.756271758469966 0.621864120765017 50 0.401094660529423 0.802189321058846 0.598905339470577 51 0.65897257958141 0.682054840837181 0.341027420418591 52 0.607616958378256 0.784766083243489 0.392383041621744 53 0.449228782028347 0.898457564056693 0.550771217971653 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 5 0.104166666666667 NOK 10% type I error level 17 0.354166666666667 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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