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

Title produced by software: Multiple Regression

Date of computation: Mon, 21 Dec 2009 02:27:51 -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/21/t1261398786hn206ogt0cxk5r0.htm/, Retrieved Mon, 21 Dec 2009 13:33:18 +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/21/t1261398786hn206ogt0cxk5r0.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}, }

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Dataseries X:

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3.2 27.6 2.7 2.5 2.4 2.6 2.8 24.9 3.2 2.7 2.5 2.4 2.8 23.8 2.8 3.2 2.7 2.5 3 24.3 2.8 2.8 3.2 2.7 3.1 23.6 3 2.8 2.8 3.2 3.1 24.2 3.1 3 2.8 2.8 3 28.1 3.1 3.1 3 2.8 2.4 30.1 3 3.1 3.1 3 2.7 31.1 2.4 3 3.1 3.1 3 32 2.7 2.4 3 3.1 2.7 32.4 3 2.7 2.4 3 2.7 34 2.7 3 2.7 2.4 2 35.1 2.7 2.7 3 2.7 2.4 37.1 2 2.7 2.7 3 2.6 37.3 2.4 2 2.7 2.7 2.4 38.1 2.6 2.4 2 2.7 2.3 39.5 2.4 2.6 2.4 2 2.4 38.3 2.3 2.4 2.6 2.4 2.5 37.3 2.4 2.3 2.4 2.6 2.6 38.7 2.5 2.4 2.3 2.4 2.6 37.5 2.6 2.5 2.4 2.3 2.6 38.7 2.6 2.6 2.5 2.4 2.7 37.9 2.6 2.6 2.6 2.5 2.8 36.6 2.7 2.6 2.6 2.6 2.6 35.5 2.8 2.7 2.6 2.6 2.6 37.6 2.6 2.8 2.7 2.6 2 38.6 2.6 2.6 2.8 2.7 2 40.3 2 2.6 2.6 2.8 2.1 39 2 2 2.6 2.6 1.9 36.8 2.1 2 2 2.6 2 36.5 1.9 2.1 2 2 2.5 34.1 2 1.9 2.1 2 2.9 34.2 2.5 2 1.9 2.1 3.3 31.9 2.9 2.5 2 1.9 3.5 33.7 3.3 2.9 2.5 2 3.8 33.5 3.5 3.3 2.9 2.5 4.6 33.8 3.8 3.5 3.3 2.9 4.4 29.9 4.6 3.8 3.5 3.3 5.3 32.3 4.4 4.6 3.8 3.5 5.8 30.5 5.3 4.4 4.6 3.8 5.9 28.5 5.8 5.3 4.4 4.6 5.6 29 5.9 5.8 5.3 4.4 5.8 23.8 5 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -0.242263576787918 + 0.0129113644924348X[t] + 1.01716594894248Y1[t] + 0.0309516297256258Y2[t] + 0.145700901873365Y3[t] -0.254856120930677Y4[t] -0.144913611898313M1[t] -0.0373589553748343M2[t] -0.0533338820604968M3[t] -0.0383076101529251M4[t] -0.0856496199108038M5[t] + 0.0022499825194379M6[t] -0.0393277493068645M7[t] -0.0827240337192012M8[t] -0.0267177690437285M9[t] + 0.0851241624145838M10[t] -0.0208085429383358M11[t] + 0.00284223045873546t + 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) -0.242263576787918 0.466128 -0.5197 0.606262 0.303131 X 0.0129113644924348 0.008178 1.5788 0.122676 0.061338 Y1 1.01716594894248 0.153438 6.6292 0 0 Y2 0.0309516297256258 0.224711 0.1377 0.891173 0.445587 Y3 0.145700901873365 0.235118 0.6197 0.539158 0.269579 Y4 -0.254856120930677 0.191886 -1.3282 0.192046 0.096023 M1 -0.144913611898313 0.281671 -0.5145 0.609898 0.304949 M2 -0.0373589553748343 0.281109 -0.1329 0.894975 0.447488 M3 -0.0533338820604968 0.28299 -0.1885 0.851515 0.425757 M4 -0.0383076101529251 0.281863 -0.1359 0.892611 0.446306 M5 -0.0856496199108038 0.281276 -0.3045 0.762406 0.381203 M6 0.0022499825194379 0.281746 0.008 0.99367 0.496835 M7 -0.0393277493068645 0.282297 -0.1393 0.889938 0.444969 M8 -0.0827240337192012 0.281583 -0.2938 0.770523 0.385262 M9 -0.0267177690437285 0.296096 -0.0902 0.928576 0.464288 M10 0.0851241624145838 0.296788 0.2868 0.77581 0.387905 M11 -0.0208085429383358 0.29656 -0.0702 0.944429 0.472215 t 0.00284223045873546 0.004341 0.6547 0.516595 0.258298 Multiple Linear Regression - Regression Statistics Multiple R 0.967681022755047 R-squared 0.936406561800253 Adjusted R-squared 0.907956865763524 F-TEST (value) 32.9144663124464 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.417141399996893 Sum Squared Residuals 6.61226400847197 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.2 2.48280208829878 0.717197911701219 2 2.8 3.13865290594126 -0.338652905941261 3 2.8 2.72358171234009 0.0764182876599137 4 3 2.75740447181290 0.242595528187096 5 3.1 2.72159150594287 0.378408494057132 6 3.1 3.02992952673895 0.0700704732610494 7 3 3.07378369023911 -0.073783690239115 8 2.4 2.92093463637734 -0.520934636377336 9 2.7 2.35381415157286 0.346185848427139 10 3 2.75212725819313 0.247872741806868 11 2.7 2.9067016736654 -0.206701673665402 12 2.7 2.85177027760573 -0.151770277605728 13 2 2.68186934247295 -0.681869342472948 14 2.4 1.98590568733908 0.414094312660918 15 2.6 2.4370123390589 0.162987660941101 16 2.4 2.57903314338655 -0.179033143386545 17 2.3 2.59204605593426 -0.292046055934260 18 2.4 2.48658506259534 -0.0865850625953439 19 2.5 2.45344822409622 0.0465517759037808 20 2.6 2.57218297229764 0.0278170277023637 21 2.6 2.76040529018814 -0.160405290188138 22 2.6 2.88276273056294 -0.282762730562939 23 2.7 2.75842764216908 -0.0584276421690752 24 2.8 2.84152462452716 -0.0415246245271623 25 2.6 2.79006250001272 -0.190062500012717 26 2.6 2.74180531580045 -0.141805315800447 27 2 2.7244781362151 -0.724478136215098 28 2 2.09937059638532 -0.0993705963853155 29 2.1 2.07048628959677 0.0295137104032333 30 1.9 2.14711917437262 -0.247119174372616 31 2 2.05708590939979 -0.0570859093997912 32 2.5 2.09564093980081 0.404359060199194 33 2.9 2.61283291636032 0.28716708363968 34 3.3 3.18570444875804 0.114295551241955 35 3.5 3.5724663002611 -0.0724663002611008 36 3.8 3.74020094272244 0.0597990572775602 37 4.6 3.86968099363554 0.730319006364462 38 4.4 4.67993953917133 -0.27993953917133 39 5.3 4.51186127809413 0.788138721905873 40 5.8 5.45585223769665 0.344147762303352 41 5.9 5.68894409351772 0.211055906482277 42 5.6 6.08543605428214 -0.485436054282144 43 5.8 5.52098677794281 0.279013222057192 44 5.5 5.48554540407665 0.0144545959233521 45 4.6 5.07294764187868 -0.472947641878682 46 4.2 4.27940556248588 -0.0794055624858843 47 4 3.66240438390442 0.337595616095578 48 3.5 3.36650415514467 0.133495844855331 49 2.3 2.87558507558001 -0.575585075580015 50 2.2 1.85369655174788 0.346303448252121 51 1.4 1.70306653429179 -0.303066534291789 52 0.6 0.908339550718588 -0.308339550718588 53 0 0.326932055008382 -0.326932055008382 54 0.5 -0.249069817989055 0.749069817989055 55 0.1 0.294695398322066 -0.194695398322066 56 0.1 0.0256960474475732 0.0743039525524268 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.312080667899929 0.624161335799858 0.687919332100071 22 0.178883854780477 0.357767709560954 0.821116145219523 23 0.120761869709832 0.241523739419665 0.879238130290168 24 0.0589785124844512 0.117957024968902 0.941021487515549 25 0.0337093905355047 0.0674187810710094 0.966290609464495 26 0.0245815141866175 0.049163028373235 0.975418485813383 27 0.0304515200273681 0.0609030400547362 0.969548479972632 28 0.0340141866977041 0.0680283733954082 0.965985813302296 29 0.0539752938866634 0.107950587773327 0.946024706113337 30 0.107660750247976 0.215321500495952 0.892339249752024 31 0.0812211482441247 0.162442296488249 0.918778851755875 32 0.0499418795001342 0.0998837590002684 0.950058120499866 33 0.0399327659222704 0.0798655318445408 0.96006723407773 34 0.0286182167648864 0.0572364335297728 0.971381783235114 35 0.0553162464618127 0.110632492923625 0.944683753538187 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 1 0.0666666666666667 NOK 10% type I error level 7 0.466666666666667 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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