*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: Fri, 26 Nov 2010 14:56:38 +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/Nov/26/t1290783320z64kgtj6q2t0ard.htm/, Retrieved Fri, 26 Nov 2010 15:55:23 +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/Nov/26/t1290783320z64kgtj6q2t0ard.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:

» Textbox « » Textfile « » CSV «

595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 0 478 0 528 0 534 0 518 0 506 0 502 0 516 1 528 1 533 1 536 1 537 1 524 1 536 1 587 1 597 1 581 1 564 1 558 1 575 1 580 1 575 1 563 1 552 1 537 1 545 1 601 1 604 1 586 1 564 1

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 Werkloosheid[t] = + 545.567567567567 + 14.3889541715629Leterme[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) 545.567567567567 6.04272 90.2851 0 0 Leterme 14.3889541715629 9.759873 1.4743 0.145809 0.072905 Multiple Linear Regression - Regression Statistics Multiple R 0.190056285612222 R-squared 0.0361213917007146 Adjusted R-squared 0.0195027950058994 F-TEST (value) 2.17355245837236 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.145809033956458 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36.7564297923929 Sum Squared Residuals 78360.0376028201 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 595 545.567567567568 49.4324324324317 2 597 545.567567567567 51.4324324324324 3 593 545.567567567568 47.4324324324324 4 590 545.567567567568 44.4324324324324 5 580 545.567567567567 34.4324324324324 6 574 545.567567567567 28.4324324324325 7 573 545.567567567567 27.4324324324325 8 573 545.567567567567 27.4324324324325 9 620 545.567567567567 74.4324324324324 10 626 545.567567567567 80.4324324324324 11 620 545.567567567567 74.4324324324324 12 588 545.567567567567 42.4324324324324 13 566 545.567567567567 20.4324324324324 14 557 545.567567567567 11.4324324324324 15 561 545.567567567567 15.4324324324324 16 549 545.567567567568 3.43243243243245 17 532 545.567567567567 -13.5675675675675 18 526 545.567567567567 -19.5675675675675 19 511 545.567567567568 -34.5675675675676 20 499 545.567567567568 -46.5675675675676 21 555 545.567567567567 9.43243243243245 22 565 545.567567567567 19.4324324324324 23 542 545.567567567567 -3.56756756756755 24 527 545.567567567567 -18.5675675675675 25 510 545.567567567568 -35.5675675675676 26 514 545.567567567568 -31.5675675675676 27 517 545.567567567568 -28.5675675675676 28 508 545.567567567568 -37.5675675675676 29 493 545.567567567568 -52.5675675675676 30 490 545.567567567567 -55.5675675675676 31 469 545.567567567567 -76.5675675675676 32 478 545.567567567567 -67.5675675675676 33 528 545.567567567567 -17.5675675675675 34 534 545.567567567567 -11.5675675675675 35 518 545.567567567568 -27.5675675675676 36 506 545.567567567568 -39.5675675675676 37 502 545.567567567568 -43.5675675675676 38 516 559.95652173913 -43.9565217391304 39 528 559.95652173913 -31.9565217391304 40 533 559.95652173913 -26.9565217391304 41 536 559.95652173913 -23.9565217391304 42 537 559.95652173913 -22.9565217391304 43 524 559.95652173913 -35.9565217391304 44 536 559.95652173913 -23.9565217391304 45 587 559.95652173913 27.0434782608696 46 597 559.95652173913 37.0434782608696 47 581 559.95652173913 21.0434782608696 48 564 559.95652173913 4.04347826086957 49 558 559.95652173913 -1.95652173913043 50 575 559.95652173913 15.0434782608696 51 580 559.95652173913 20.0434782608696 52 575 559.95652173913 15.0434782608696 53 563 559.95652173913 3.04347826086957 54 552 559.95652173913 -7.95652173913044 55 537 559.95652173913 -22.9565217391304 56 545 559.95652173913 -14.9565217391304 57 601 559.95652173913 41.0434782608696 58 604 559.95652173913 44.0434782608696 59 586 559.95652173913 26.0434782608696 60 564 559.95652173913 4.04347826086957 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0138568097279648 0.0277136194559295 0.986143190272035 6 0.0129576744090749 0.0259153488181499 0.987042325590925 7 0.00808433686782365 0.0161686737356473 0.991915663132176 8 0.00419624271076132 0.00839248542152265 0.995803757289239 9 0.0275889956197443 0.0551779912394886 0.972411004380256 10 0.095287641847316 0.190575283694632 0.904712358152684 11 0.170017701480021 0.340035402960043 0.829982298519979 12 0.156492357697739 0.312984715395479 0.84350764230226 13 0.197976752404062 0.395953504808124 0.802023247595938 14 0.279730358928445 0.55946071785689 0.720269641071555 15 0.332281495580704 0.664562991161408 0.667718504419296 16 0.437939285473488 0.875878570946975 0.562060714526513 17 0.6224866407424 0.7550267185152 0.3775133592576 18 0.759809138008306 0.480381723983389 0.240190861991694 19 0.884307990027579 0.231384019944842 0.115692009972421 20 0.956230788810548 0.0875384223789047 0.0437692111894523 21 0.95688577314139 0.0862284537172189 0.0431142268586094 22 0.96873830540801 0.0625233891839796 0.0312616945919898 23 0.971273600439416 0.0574527991211689 0.0287263995605844 24 0.97386193211453 0.0522761357709409 0.0261380678854704 25 0.979755988131775 0.0404880237364496 0.0202440118682248 26 0.981330550418401 0.037338899163197 0.0186694495815985 27 0.98106526717528 0.0378694656494415 0.0189347328247208 28 0.981634401027251 0.0367311979454977 0.0183655989727488 29 0.985695655040536 0.0286086899189283 0.0143043449594641 30 0.988592885058744 0.0228142298825122 0.0114071149412561 31 0.995975360224538 0.00804927955092397 0.00402463977546198 32 0.997968114417173 0.00406377116565445 0.00203188558282722 33 0.996654015085783 0.00669196982843345 0.00334598491421672 34 0.995219013243343 0.0095619735133138 0.0047809867566569 35 0.99273272326394 0.0145345534721188 0.0072672767360594 36 0.989405835793874 0.0211883284122521 0.010594164206126 37 0.9849316456749 0.0301367086502003 0.0150683543251001 38 0.988540343629136 0.022919312741729 0.0114596563708645 39 0.98840320294586 0.0231935941082795 0.0115967970541398 40 0.98726838726387 0.0254632254722588 0.0127316127361294 41 0.985640980405896 0.028718039188208 0.014359019594104 42 0.98435005214343 0.0312998957131383 0.0156499478565691 43 0.99199866097685 0.0160026780462996 0.00800133902314979 44 0.994236980418622 0.0115260391627565 0.00576301958137823 45 0.992012544126432 0.0159749117471358 0.00798745587356788 46 0.992467675750585 0.0150646484988309 0.00753232424941543 47 0.98691661690773 0.026166766184539 0.0130833830922695 48 0.974743335130532 0.0505133297389367 0.0252566648694684 49 0.956636253911595 0.0867274921768104 0.0433637460884052 50 0.92269957502196 0.154600849956078 0.0773004249780392 51 0.874266165781431 0.251467668437138 0.125733834218569 52 0.795455155926458 0.409089688147085 0.204544844073542 53 0.68363873581623 0.632722528367541 0.31636126418377 54 0.578035974348047 0.843928051303906 0.421964025651953 55 0.610794079362074 0.778411841275853 0.389205920637926 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0980392156862745 NOK 5% type I error level 27 0.529411764705882 NOK 10% type I error level 35 0.686274509803922 NOK

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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