ws7

*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, 26 Dec 2009 11:13:42 -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/Dec/26/t1261851272uhl8cpyjzk1owj5.htm/, Retrieved Sat, 26 Dec 2009 19:14:44 +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/26/t1261851272uhl8cpyjzk1owj5.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:

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No (this computation is public)

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Dataseries X:

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1.2 2.2 1.4 1.1 1.2 1.3 1.5 2.3 1.2 1.4 1.1 1.2 1.1 2.3 1.5 1.2 1.4 1.1 1.3 2.2 1.1 1.5 1.2 1.4 1.5 2.2 1.3 1.1 1.5 1.2 1.1 1.6 1.5 1.3 1.1 1.5 1.4 1.8 1.1 1.5 1.3 1.1 1.3 1.7 1.4 1.1 1.5 1.3 1.5 1.9 1.3 1.4 1.1 1.5 1.6 1.8 1.5 1.3 1.4 1.1 1.7 1.9 1.6 1.5 1.3 1.4 1.1 1.5 1.7 1.6 1.5 1.3 1.6 1 1.1 1.7 1.6 1.5 1.3 0.8 1.6 1.1 1.7 1.6 1.7 1.1 1.3 1.6 1.1 1.7 1.6 1.5 1.7 1.3 1.6 1.1 1.7 1.7 1.6 1.7 1.3 1.6 1.9 2.3 1.7 1.6 1.7 1.3 1.8 2.4 1.9 1.7 1.6 1.7 1.9 3 1.8 1.9 1.7 1.6 1.6 3 1.9 1.8 1.9 1.7 1.5 3.2 1.6 1.9 1.8 1.9 1.6 3.2 1.5 1.6 1.9 1.8 1.6 3.2 1.6 1.5 1.6 1.9 1.7 3.5 1.6 1.6 1.5 1.6 2 4 1.7 1.6 1.6 1.5 2 4.3 2 1.7 1.6 1.6 1.9 4.1 2 2 1.7 1.6 1.7 4 1.9 2 2 1.7 1.8 4.1 1.7 1.9 2 2 1.9 4.2 1.8 1.7 1.9 2 1.7 4.5 1.9 1.8 1.7 1.9 2 5.6 1.7 1.9 1.8 1.7 2.1 6.5 2 1.7 1.9 1.8 2.4 7.6 2.1 2 1.7 1.9 2.5 8.5 2.4 2.1 2 1.7 2.5 8.7 2.5 2.4 2.1 2 2.6 8.3 2.5 2.5 2.4 2.1 2.2 8.3 2.6 2.5 2.5 2.4 2.5 8.5 2.2 2.6 2.5 2.5 2.8 8.7 2.5 2.2 2.6 2.5 2.8 8.7 2.8 2.5 2.2 2.6 2.9 8.5 2.8 2. 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 0.445876947317449 + 0.0630464964599403X[t] + 0.333944163747943Y1[t] + 0.330677338008161Y2[t] -0.156978631392103Y3[t] + 0.0624645597720463Y4[t] + 0.00560319987550132t + 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) 0.445876947317449 0.154899 2.8785 0.00595 0.002975 X 0.0630464964599403 0.015138 4.1649 0.000129 6.4e-05 Y1 0.333944163747943 0.139541 2.3932 0.020664 0.010332 Y2 0.330677338008161 0.146354 2.2594 0.028433 0.014217 Y3 -0.156978631392103 0.146334 -1.0727 0.28875 0.144375 Y4 0.0624645597720463 0.137012 0.4559 0.650514 0.325257 t 0.00560319987550132 0.004337 1.292 0.202532 0.101266 Multiple Linear Regression - Regression Statistics Multiple R 0.936908177184696 R-squared 0.87779693247555 Adjusted R-squared 0.862521549034993 F-TEST (value) 57.4648051154637 F-TEST (DF numerator) 6 F-TEST (DF denominator) 48 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.197210679275923 Sum Squared Residuals 1.86681849698261 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.2 1.31427891049405 -0.114278910494052 2 1.5 1.36805253583041 0.131947464169587 3 1.1 1.35436347183383 -0.254363471833830 4 1.3 1.36942265217664 -0.0694226521766431 5 1.5 1.24995724822643 0.250042751773572 6 1.1 1.43218767106564 -0.332187671065641 7 1.4 1.32657642214835 0.0734235778516534 8 1.3 1.27488447197496 0.0251155280250395 9 1.5 1.43419012068135 0.0658098793186456 10 1.6 1.39513035653318 0.204869643466815 11 1.7 1.54100532110193 0.158994678898069 12 1.1 1.55020989031344 -0.450209890313441 13 1.6 1.35378612632622 0.246213873673778 14 1.3 1.30589429881680 -0.0058942988168041 15 1.7 1.49600050232245 0.203999497677548 16 1.6 1.44522871331938 0.154771286680622 17 1.7 1.64064360061899 0.0593563993810077 18 1.9 1.60287056045598 0.297129439544019 19 1.8 1.75531866357591 0.0446813364240905 20 1.9 1.8095464934378 0.0904535065622017 21 1.6 1.79032710558606 -0.190327105586062 22 1.5 1.76961486452360 -0.269614864523604 23 1.6 1.62067612750545 -0.0206761275054478 24 1.6 1.67994605534976 -0.0799460553497627 25 1.7 1.73448943317166 -0.0344894331716588 26 2 1.78306597853551 0.216934021464490 27 2 1.94708056625140 0.0529194337486037 28 1.9 2.02357980509815 -0.123579805098148 29 1.7 1.94863680551243 -0.248636805512435 30 1.8 1.87942745641514 -0.0794274564151391 31 1.9 1.87429211784901 0.0257078821509930 32 1.7 1.99042068713932 -0.290420687139317 33 2 2.00346315907836 -0.00346315907836029 34 2.1 2.09040458012855 0.00959541987144743 35 2.4 2.33559872614286 0.0644012738571437 36 2.5 2.47160825438546 0.0283917456145374 37 2.5 2.6254598761226 -0.125459876122598 38 2.6 2.59806507777451 0.00193492222548675 39 2.2 2.64010419881721 -0.440104198817212 40 2.5 2.56405322226355 -0.0640532222635459 41 2.8 2.53448017221294 0.265519827787057 42 2.8 2.80850773114932 -0.00850773114932122 43 2.9 2.82862541980883 0.0713745801911665 44 3 2.80144091669715 0.198559083302852 45 3.1 2.83550378786593 0.264496212134073 46 2.9 2.8162154790259 0.0837845209740996 47 2.7 2.6966857273927 0.00331427260729896 48 2.2 2.50947602258702 -0.309476022587024 49 2.5 2.28178595736658 0.218214042633417 50 2.3 2.21591795310242 0.0840820468975784 51 2.6 2.29471332678845 0.305286673211552 52 2.3 2.22451519065308 0.0754848093469237 53 2.2 2.26035948807870 -0.0603594880786954 54 1.8 2.05486461986693 -0.254864619866932 55 1.8 1.94704607849970 -0.147046078499697 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.211420173856209 0.422840347712417 0.788579826143791 11 0.31802405503939 0.63604811007878 0.68197594496061 12 0.268439643709498 0.536879287418996 0.731560356290502 13 0.542903819448485 0.91419236110303 0.457096180551515 14 0.422274292694362 0.844548585388724 0.577725707305638 15 0.328467881227638 0.656935762455277 0.671532118772362 16 0.246861540264447 0.493723080528893 0.753138459735553 17 0.182705144518865 0.365410289037730 0.817294855481135 18 0.176205126638044 0.352410253276088 0.823794873361956 19 0.118264932624138 0.236529865248277 0.881735067375862 20 0.114249372285798 0.228498744571596 0.885750627714202 21 0.170902093755159 0.341804187510319 0.82909790624484 22 0.432982529268914 0.865965058537827 0.567017470731086 23 0.447121642691358 0.894243285382716 0.552878357308642 24 0.42911722975912 0.85823445951824 0.57088277024088 25 0.411004852454363 0.822009704908726 0.588995147545637 26 0.438973211764935 0.87794642352987 0.561026788235065 27 0.376894933912173 0.753789867824346 0.623105066087827 28 0.313094096623238 0.626188193246476 0.686905903376762 29 0.281534701854143 0.563069403708287 0.718465298145857 30 0.214726329429644 0.429452658859288 0.785273670570356 31 0.177490287637738 0.354980575275476 0.822509712362262 32 0.21190609104764 0.42381218209528 0.78809390895236 33 0.167982618314296 0.335965236628592 0.832017381685704 34 0.133482519829578 0.266965039659156 0.866517480170422 35 0.131485943545401 0.262971887090802 0.868514056454599 36 0.128991360033838 0.257982720067677 0.871008639966162 37 0.0927168141348684 0.185433628269737 0.907283185865132 38 0.125835433180092 0.251670866360183 0.874164566819909 39 0.207861712912317 0.415723425824633 0.792138287087683 40 0.184035224654684 0.368070449309368 0.815964775345316 41 0.230181162882447 0.460362325764894 0.769818837117553 42 0.5498234619782 0.9003530760436 0.4501765380218 43 0.743142415358971 0.513715169282058 0.256857584641029 44 0.890179813533516 0.219640372932969 0.109820186466484 45 0.850979934350582 0.298040131298837 0.149020065649419 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 = 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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