*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: Sat, 11 Dec 2010 16:17:47 +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/11/t1292084202daxzlkdm56lglmn.htm/, Retrieved Sat, 11 Dec 2010 17:16:45 +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/11/t1292084202daxzlkdm56lglmn.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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1 7 6,3 4,5 42 3 1 3 2.547 4.603 2,1 69 624 3 5 4 11 180 9,1 27 180 4 4 4 0,023 0,3 15,8 19 35 1 1 1 160 169 5,2 30,4 392 4 5 4 3 26 10,9 28 63 1 2 1 52 440 8,3 50 230 1 1 1 0,425 6 11 7 112 5 4 4 465 423 3,2 30 281 5 5 5 0,075 1 6,3 3,5 42 1 1 1 3 25 8,6 50 28 2 2 2 0,785 4 6,6 6 42 2 2 2 0,2 5 9,5 10,4 120 2 2 2 28 115 3,3 20 148 5 5 5 0,12 1 11 3,9 16 3 1 2 85 325 4,7 41 310 1 3 1 0,101 4 10,4 9 28 5 1 3 1 6 7,4 7,6 68 5 3 4 521 655 2,1 46 336 5 5 5 0,005 0,14 7,7 2,6 21,5 5 2 4 0,01 0,25 17,9 24 50 1 1 1 62 1.320 6,1 100 267 1 1 1 0,023 0,4 11,9 3,2 19 4 1 3 0,048 0,33 10,8 2 30 4 1 3 2 6 13,8 5 12 2 1 1 4 11 14,3 6,5 120 2 1 1 0,48 16 15,2 12 140 2 2 2 10 115 10 20,2 170 4 4 4 2 11 11,9 13 17 2 1 2 192 180 6,5 27 115 4 4 4 3 12 7,5 18 31 5 5 5 0,28 2 10,6 4,7 21 3 1 3 4 50 7,4 9,8 52 1 1 1 7 179 8,4 29 164 2 3 2 0,75 12 5,7 7 225 2 2 2 4 21 4,9 6 225 3 2 3 56 175 3,2 20 151 5 5 5 0,9 3 11 4,5 60 2 1 2 2 12 4,9 7,5 200 3 1 3 0,104 3 13,2 2,3 46 3 2 2 4 58 9,7 24 210 etc...

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 12.7894647555942 -0.000920360007190503Wb[t] -0.00407543480665229Wbr[t] -0.00545130109419674L[t] -0.0102385857977621Tg[t] + 1.43725443584876P[t] + 0.436070831135465S[t] -2.79782099005727D[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) 12.7894647555942 1.271119 10.0616 0 0 Wb -0.000920360007190503 0.00749 -0.1229 0.902921 0.45146 Wbr -0.00407543480665229 0.005843 -0.6974 0.490272 0.245136 L -0.00545130109419674 0.030974 -0.176 0.86134 0.43067 Tg -0.0102385857977621 0.005506 -1.8597 0.071604 0.035802 P 1.43725443584876 1.01571 1.415 0.166156 0.083078 S 0.436070831135465 0.613711 0.7105 0.48221 0.241105 D -2.79782099005727 1.260299 -2.22 0.033193 0.016596 Multiple Linear Regression - Regression Statistics Multiple R 0.741625986682653 R-squared 0.550009104123018 Adjusted R-squared 0.457363919677757 F-TEST (value) 5.93672631142516 F-TEST (DF numerator) 7 F-TEST (DF denominator) 34 p-value 0.00014631561076639 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.82680337537443 Sum Squared Residuals 271.68778898296 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 8.6598360620205 -2.35983606202049 2 2.1 1.3041775619323 0.795822438067702 3 9.1 6.35764906488505 2.74235093511495 4 15.8 11.4018000100876 4.39819998991242 5 5.2 4.51230142497647 0.687698575023526 6 10.9 11.3946501427656 -0.494650142765568 7 8.3 7.39647920902513 0.903520790974872 8 11 9.3190118202991 1.6809881797009 9 3.2 2.97452817167446 0.225471828325545 10 6.3 11.4117244133783 -5.11172441337827 11 8.6 10.2765809022131 -1.67658090221306 12 6.6 10.4607206775447 -3.86072067754467 13 9.5 9.63458823630232 -0.134588236302321 14 3.3 6.04820433730993 -2.74820433730993 15 11 11.7523935891223 -0.752393589122338 16 4.7 7.93689883985059 -3.23689883985059 17 10.4 11.6662079880292 -1.26620798802923 18 7.4 9.32963877660452 -1.92963877660452 19 2.1 1.3271440997444 0.772855900255604 20 7.7 9.4217164967101 -1.72171649671011 21 17.9 11.2211804540706 6.6788195459294 22 6.1 8.52369462070842 -2.42369462070842 23 11.9 10.3674617240912 1.53253827590882 24 10.8 10.2616411130651 0.538358886934887 25 13.8 13.1258106044715 0.67418939552851 26 14.3 11.9896484926242 2.31035150737575 27 15.2 9.37600695492118 5.82399304507882 28 10 6.7629273927428 3.23707260725721 29 11.9 10.2128091026386 1.68719089736142 30 6.5 6.8565719804381 -0.356571980438101 31 7.5 7.69980026310144 -0.199800263101435 32 10.6 8.8947959367931 1.7052040632069 33 7.4 11.071686639953 -3.67168663995302 34 8.4 8.8033829875778 -0.403382987577802 35 5.7 8.54903690960705 -2.84903690960705 36 4.9 7.1542515732095 -2.25425157320951 37 3.2 5.74719241131617 -2.54719241131617 38 11 9.85250184709661 1.14749815290339 39 4.9 7.00448806865105 -2.10448806865105 40 13.2 11.8818927842225 1.31810721577753 41 9.7 6.13442012956122 3.56557987043878 42 12.8 13.1225461846633 -0.322546184663286 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.856868583750217 0.286262832499565 0.143131416249782 12 0.845675728554153 0.308648542891695 0.154324271445847 13 0.754751096787312 0.490497806425375 0.245248903212688 14 0.69444830114245 0.6111033977151 0.30555169885755 15 0.600845054765997 0.798309890468006 0.399154945234003 16 0.615677393970328 0.768645212059343 0.384322606029672 17 0.552557319840022 0.894885360319956 0.447442680159978 18 0.461189679929969 0.922379359859939 0.538810320070031 19 0.386077796341983 0.772155592683966 0.613922203658017 20 0.309751836622774 0.619503673245549 0.690248163377226 21 0.696441628799634 0.607116742400732 0.303558371200366 22 0.833507766906959 0.332984466186082 0.166492233093041 23 0.768032243482033 0.463935513035934 0.231967756517967 24 0.676908420262236 0.646183159475529 0.323091579737764 25 0.572910953347738 0.854178093304525 0.427089046652262 26 0.472124245771711 0.944248491543422 0.527875754228289 27 0.839199431853468 0.321601136293064 0.160800568146532 28 0.916626373141186 0.166747253717629 0.0833736268588143 29 0.840248852597185 0.31950229480563 0.159751147402815 30 0.738157753068605 0.52368449386279 0.261842246931395 31 0.905481060936367 0.189037878127266 0.0945189390636328 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 = 3 ; 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') }

Copyright

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Software written by Ed van Stee & Patrick Wessa

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• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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