*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 23 Nov 2008 11:48:48 -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/Nov/23/t1227466353vws7kmksu7b4gbs.htm/, Retrieved Sun, 23 Nov 2008 18:52:52 +0000

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/Nov/23/t1227466353vws7kmksu7b4gbs.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}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

rente en woongebouwen

Dataseries X:

» Textbox « » Textfile « » CSV «

16 0 8 0 -10 0 -24 0 -19 0 8 0 24 0 14 0 7 0 9 0 -26 0 19 0 15 0 -1 0 -10 0 -21 0 -14 0 -27 0 26 0 23 0 5 0 19 0 -19 0 24 0 17 0 1 0 -9 0 -16 0 -21 0 -14 0 31 0 27 0 10 0 12 0 -23 0 13 0 26 0 -1 0 4 0 -16 0 -5 0 9 0 23 0 9 0 2 0 10 1 -29 1 17 1 9 1 9 1 -10 1 -23 1 13 1 13 1 -9 1 9 1 5 1 8 1 -18 1 7 1 4 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation x[t] = + 2.80434782608695 -2.07101449275362y[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) 2.80434782608695 2.41084 1.1632 0.249422 0.124711 y -2.07101449275362 4.861694 -0.426 0.671668 0.335834 Multiple Linear Regression - Regression Statistics Multiple R 0.0553735830765855 R-squared 0.00306623370273951 Adjusted R-squared -0.0138309487768751 F-TEST (value) 0.181464200107843 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.671668010767671 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16.3511117456307 Sum Squared Residuals 15774.1724637681 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16 2.80434782608697 13.1956521739130 2 8 2.80434782608696 5.19565217391304 3 -10 2.80434782608696 -12.8043478260870 4 -24 2.80434782608696 -26.8043478260870 5 -19 2.80434782608696 -21.8043478260870 6 8 2.80434782608696 5.19565217391304 7 24 2.80434782608696 21.1956521739130 8 14 2.80434782608696 11.1956521739130 9 7 2.80434782608696 4.19565217391304 10 9 2.80434782608696 6.19565217391304 11 -26 2.80434782608696 -28.8043478260870 12 19 2.80434782608696 16.1956521739130 13 15 2.80434782608696 12.1956521739130 14 -1 2.80434782608696 -3.80434782608696 15 -10 2.80434782608696 -12.8043478260870 16 -21 2.80434782608696 -23.8043478260870 17 -14 2.80434782608696 -16.8043478260870 18 -27 2.80434782608696 -29.8043478260870 19 26 2.80434782608696 23.1956521739130 20 23 2.80434782608696 20.1956521739130 21 5 2.80434782608696 2.19565217391304 22 19 2.80434782608696 16.1956521739130 23 -19 2.80434782608696 -21.8043478260870 24 24 2.80434782608696 21.1956521739130 25 17 2.80434782608696 14.1956521739130 26 1 2.80434782608696 -1.80434782608696 27 -9 2.80434782608696 -11.8043478260870 28 -16 2.80434782608696 -18.8043478260870 29 -21 2.80434782608696 -23.8043478260870 30 -14 2.80434782608696 -16.8043478260870 31 31 2.80434782608696 28.1956521739130 32 27 2.80434782608696 24.1956521739130 33 10 2.80434782608696 7.19565217391304 34 12 2.80434782608696 9.19565217391304 35 -23 2.80434782608696 -25.8043478260870 36 13 2.80434782608696 10.1956521739130 37 26 2.80434782608696 23.1956521739130 38 -1 2.80434782608696 -3.80434782608696 39 4 2.80434782608696 1.19565217391304 40 -16 2.80434782608696 -18.8043478260870 41 -5 2.80434782608696 -7.80434782608696 42 9 2.80434782608696 6.19565217391304 43 23 2.80434782608696 20.1956521739130 44 9 2.80434782608696 6.19565217391304 45 2 2.80434782608696 -0.804347826086957 46 10 0.73333333333333 9.26666666666667 47 -29 0.733333333333334 -29.7333333333333 48 17 0.73333333333333 16.2666666666667 49 9 0.73333333333333 8.26666666666667 50 9 0.73333333333333 8.26666666666667 51 -10 0.73333333333333 -10.7333333333333 52 -23 0.733333333333334 -23.7333333333333 53 13 0.73333333333333 12.2666666666667 54 13 0.73333333333333 12.2666666666667 55 -9 0.73333333333333 -9.73333333333333 56 9 0.73333333333333 8.26666666666667 57 5 0.733333333333332 4.26666666666667 58 8 0.73333333333333 7.26666666666667 59 -18 0.733333333333334 -18.7333333333333 60 7 0.73333333333333 6.26666666666667 61 4 2.80434782608696 1.19565217391304 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.77768647243525 0.444627055129499 0.222313527564749 6 0.703313422348229 0.593373155303542 0.296686577651771 7 0.797662149333872 0.404675701332255 0.202337850666128 8 0.745936600944386 0.508126798111228 0.254063399055614 9 0.648611720105674 0.702776559788653 0.351388279894326 10 0.552079467987945 0.89584106402411 0.447920532012055 11 0.715124802505737 0.569750394988526 0.284875197494263 12 0.711863794289398 0.576272411421204 0.288136205710602 13 0.668679144246975 0.66264171150605 0.331320855753025 14 0.583868814286602 0.832262371426796 0.416131185713398 15 0.54248025423869 0.91503949152262 0.45751974576131 16 0.613654594010238 0.772690811979524 0.386345405989762 17 0.598676868070289 0.802646263859422 0.401323131929711 18 0.732160225255396 0.535679549489207 0.267839774744604 19 0.804564201601688 0.390871596796624 0.195435798398312 20 0.832307231940524 0.335385536118953 0.167692768059476 21 0.779381314926552 0.441237370146895 0.220618685073448 22 0.775804237218586 0.448391525562828 0.224195762781414 23 0.810127209131335 0.379745581737331 0.189872790868665 24 0.838930276107508 0.322139447784984 0.161069723892492 25 0.824380303943188 0.351239392113625 0.175619696056812 26 0.771170981981584 0.457658036036832 0.228829018018416 27 0.741118266450064 0.517763467099872 0.258881733549936 28 0.759175877930827 0.481648244138346 0.240824122069173 29 0.82424110938366 0.351517781232679 0.175758890616339 30 0.837453489767148 0.325093020465705 0.162546510232852 31 0.903457223557229 0.193085552885543 0.0965427764427713 32 0.932092429426464 0.135815141147072 0.0679075705735358 33 0.90796323030029 0.184073539399418 0.092036769699709 34 0.882568390911258 0.234863218177484 0.117431609088742 35 0.939105448537953 0.121789102924094 0.0608945514620471 36 0.920032263900925 0.15993547219815 0.079967736099075 37 0.944914602339573 0.110170795320855 0.0550853976604274 38 0.920694191349138 0.158611617301725 0.0793058086508623 39 0.886020660777996 0.227958678444007 0.113979339222004 40 0.912254545225045 0.175490909549909 0.0877454547749545 41 0.898156625347675 0.20368674930465 0.101843374652325 42 0.85665057787148 0.286698844257042 0.143349422128521 43 0.863074366335781 0.273851267328437 0.136925633664219 44 0.81467977022622 0.370640459547561 0.185320229773781 45 0.7485088340359 0.502982331928199 0.251491165964099 46 0.693184393800464 0.613631212399072 0.306815606199536 47 0.872518494920532 0.254963010158935 0.127481505079468 48 0.88089087292338 0.238218254153241 0.119109127076620 49 0.839903858646113 0.320192282707774 0.160096141353887 50 0.791224615364238 0.417550769271523 0.208775384635762 51 0.74180018872097 0.51639962255806 0.25819981127903 52 0.886805125590606 0.226389748818788 0.113194874409394 53 0.854435835265529 0.291128329468942 0.145564164734471 54 0.827082572682048 0.345834854635903 0.172917427317952 55 0.771104984829311 0.457790030341378 0.228895015170689 56 0.655647009047579 0.688705981904842 0.344352990952421 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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