MLRM 1

*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: Wed, 15 Dec 2010 16:03:07 +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/15/t1292428900kj8dr8vakpwrpo6.htm/, Retrieved Wed, 15 Dec 2010 17:01:50 +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/15/t1292428900kj8dr8vakpwrpo6.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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6.3 2 4.5 1 6.6 42 3 1 3 2.1 1.8 69 2547 4603 624 3 5 4 9.1 0.7 27 10.55 179.5 180 4 4 4 15.8 3.9 19 0.023 0.3 35 1 1 1 5.2 1 30.4 160 169 392 4 5 4 10.9 3.6 28 3.3 25.6 63 1 2 1 8.3 1.4 50 52.16 440 230 1 1 1 11 1.5 7 0.425 6.4 112 5 4 4 3.2 0.7 30 465 423 281 5 5 5 6.3 2.1 3.5 0.075 1.2 42 1 1 1 8.6 0 50 3 25 28 2 2 2 6.6 4.1 6 0.785 3.5 42 2 2 2 9.5 1.2 10.4 0.2 5 120 2 2 2 3.3 0.5 20 27.66 115 148 5 5 5 11 3.4 3.9 0.12 1 16 3 1 2 4.7 1.5 41 85 325 310 1 3 1 10.4 3.4 9 0.101 4 28 5 1 3 7.4 0.8 7.6 1.04 5.5 68 5 3 4 2.1 0.8 46 521 655 336 5 5 5 7.7 1.4 2.6 0.005 0.14 21.5 5 2 4 17.9 2 24 0.01 0.25 50 1 1 1 6.1 1.9 100 62 1320 267 1 1 1 11.9 1.3 3.2 0.023 0.4 19 4 1 3 10.8 2 2 0.048 0.33 30 4 1 3 13.8 5.6 5 1.7 6.3 12 2 1 1 14.3 3.1 6.5 3.5 10.8 120 2 1 1 10 0.9 20.2 10 115 170 4 4 4 11.9 1.8 13 1.62 11.4 17 2 1 2 6.5 1.9 27 192 180 115 4 4 4 7.5 0.9 18 2.5 12.1 31 5 5 5 10.6 2.6 4.7 0.28 1.9 21 3 1 3 7.4 2.4 9.8 4.235 50.4 52 1 1 1 8.4 1.2 29 6.8 179 164 2 3 2 5.7 0.9 7 0.75 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 12.3197087181946 + 0.142634167491983PS[t] + 0.0110188228044140LS[t] + 0.00358575159323686BW[t] -0.00147763369106797BRW[t] -0.0142418480170465GT[t] + 1.51015954701529PI[t] + 0.137314401734720SEI[t] -2.67140908301206ODI[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) 12.3197087181946 2.239418 5.5013 5e-06 2e-06 PS 0.142634167491983 0.49663 0.2872 0.775808 0.387904 LS 0.0110188228044140 0.042204 0.2611 0.795699 0.39785 BW 0.00358575159323686 0.005347 0.6706 0.507257 0.253628 BRW -0.00147763369106797 0.003185 -0.4639 0.645861 0.32293 GT -0.0142418480170465 0.006737 -2.1141 0.042394 0.021197 PI 1.51015954701529 1.078434 1.4003 0.171038 0.085519 SEI 0.137314401734720 0.638624 0.215 0.831119 0.41556 ODI -2.67140908301206 1.489998 -1.7929 0.082448 0.041224 Multiple Linear Regression - Regression Statistics Multiple R 0.760338768848172 R-squared 0.578115043413554 Adjusted R-squared 0.472643804266942 F-TEST (value) 5.48125771623805 F-TEST (DF numerator) 8 F-TEST (DF denominator) 32 p-value 0.000214898271983843 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.71971430821945 Sum Squared Residuals 236.699069386675 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 8.70380330205908 -2.40380330205908 2 2.1 1.31261157620734 0.787388423792664 3 9.1 5.83038210280354 3.26961789719646 4 15.8 11.5625789720178 4.23742102798217 5 5.2 3.58008470207246 1.61991529792754 6 10.9 11.3318671598544 -0.431867159854397 7 8.3 8.30765149375464 -0.00765149375463509 8 11 8.42219084992565 2.57780915007436 9 3.2 4.67081779500448 -1.47081779500448 10 6.3 11.0342093697054 -4.73420936970541 11 8.6 10.3978242579169 -1.7978242579169 12 6.6 10.3222369535801 -3.72223695358011 13 9.5 8.8419024276445 0.6580975723555 14 3.3 5.31318709479185 -2.01318709479185 15 11 11.9436962615884 -0.943696261588399 16 4.7 7.64571042416454 -2.94571042416454 17 10.4 12.1733990623514 -1.77339906235140 18 7.4 8.82182024493103 -1.42182024493103 19 2.1 3.93607180858023 -1.83607180858023 20 7.7 9.38144702614722 -1.68144702614722 21 17.9 11.1330677144633 6.76693228553672 22 6.1 7.13792748862824 -1.03792748862825 23 11.9 10.4330150161543 1.46698498384567 24 10.8 10.3631690959941 0.43683090400588 25 13.8 13.4856630921752 0.314336907824777 26 14.3 11.6072913230689 2.69270867693112 27 10 6.01973463109999 3.98026536890001 28 11.9 10.2813627230918 1.6186372769082 29 6.5 7.57715903464924 -1.07715903464924 30 7.5 7.07633033089932 0.42366966910068 31 10.6 9.095029512674 1.50497048732599 32 7.4 10.9462168724777 -3.54621687247767 33 8.4 8.32408331906081 0.0759166809391907 34 5.7 7.2574395755035 -1.55743957550350 35 4.9 6.02548152863396 -1.12548152863396 36 3.2 5.29589427038155 -2.09589427038155 37 11 9.65704178360154 1.34295821639846 38 4.9 6.26785977209513 -1.36785977209513 39 13.2 11.5197439497690 1.68025605023102 40 9.7 5.37521948872675 4.32478051127325 41 12.8 13.5877765917507 -0.787776591750676 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.938246797034884 0.123506405930233 0.0617532029651163 13 0.926200872666933 0.147598254666134 0.073799127333067 14 0.896848168459703 0.206303663080595 0.103151831540297 15 0.845601803851158 0.308796392297684 0.154398196148842 16 0.89591461264315 0.208170774713701 0.104085387356850 17 0.929918303588323 0.140163392823355 0.0700816964116775 18 0.904654847333977 0.190690305332047 0.0953451526660234 19 0.902742669696241 0.194514660607519 0.0972573303037594 20 0.889560178716122 0.220879642567756 0.110439821283878 21 0.971668670283401 0.0566626594331978 0.0283313297165989 22 0.946262751586848 0.107474496826304 0.0537372484131521 23 0.910475834290852 0.179048331418296 0.0895241657091479 24 0.887708149214981 0.224583701570038 0.112291850785019 25 0.813391378192087 0.373217243615827 0.186608621807913 26 0.730130563078931 0.539738873842138 0.269869436921069 27 0.849447750928149 0.301104498143703 0.150552249071851 28 0.731914639227026 0.536170721545948 0.268085360772974 29 0.5723244808622 0.8553510382756 0.4276755191378 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 1 0.0555555555555556 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• 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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