*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, 20 Nov 2009 06:03:10 -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/Nov/20/t1258722261898zs9ms1sgfxgm.htm/, Retrieved Fri, 20 Nov 2009 14:04:33 +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/Nov/20/t1258722261898zs9ms1sgfxgm.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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2.155 22.782 2.172 19.169 2.15 13.807 2.533 29.743 2.058 25.591 2.16 29.096 2.26 26.482 2.498 22.405 2.695 27.044 2.799 17.97 2.947 18.73 2.93 19.684 2.318 19.785 2.54 18.479 2.57 10.698 2.669 31.956 2.45 29.506 2.842 34.506 3.44 27.165 2.678 26.736 2.981 23.691 2.26 18.157 2.844 17.328 2.546 18.205 2.456 20.995 2.295 17.382 2.379 9.367 2.479 31.124 2.057 26.551 2.28 30.651 2.351 25.859 2.276 25.1 2.548 25.778 2.311 20.418 2.201 18.688 2.725 20.424 2.408 24.776 2.139 19.814 1.898 12.738 2.537 31.566 2.069 30.111 2.063 30.019 2.524 31.934 2.437 25.826 2.189 26.835 2.793 20.205 2.074 17.789 2.622 20.52 2.278 22.518 2.144 15.572 2.427 11.509 2.139 25.447 1.828 24.09 2.072 27.786 1.8 26.195 1.758 20.516 2.246 22.759 1.987 19.028 1.868 16.971 2.514 20.036 2.121 22.485

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation geb[t] = + 2.18467317439167 + 0.0393570170256916aut[t] -0.515522739837599M1[t] -0.424949404142556M2[t] -0.135718050654185M3[t] -0.662850919050637M4[t] -0.923544961910348M5[t] -0.851923901991616M6[t] -0.538586012966687M7[t] -0.54175420438965M8[t] -0.374627199087015M9[t] -0.229486767499956M10[t] -0.215108687630309M11[t] -0.00820863771261903t + 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) 2.18467317439167 0.42263 5.1692 5e-06 2e-06 aut 0.0393570170256916 0.019602 2.0079 0.050427 0.025213 M1 -0.515522739837599 0.170905 -3.0164 0.004119 0.002059 M2 -0.424949404142556 0.176354 -2.4096 0.019937 0.009969 M3 -0.135718050654185 0.236876 -0.5729 0.569411 0.284705 M4 -0.662850919050637 0.261951 -2.5304 0.014801 0.0074 M5 -0.923544961910348 0.223612 -4.1301 0.000148 7.4e-05 M6 -0.851923901991616 0.26883 -3.169 0.00269 0.001345 M7 -0.538586012966687 0.228334 -2.3588 0.022545 0.011273 M8 -0.54175420438965 0.191054 -2.8356 0.006725 0.003362 M9 -0.374627199087015 0.201596 -1.8583 0.069395 0.034697 M10 -0.229486767499956 0.171965 -1.3345 0.188471 0.094235 M11 -0.215108687630309 0.175407 -1.2263 0.22618 0.11309 t -0.00820863771261903 0.002023 -4.0576 0.000186 9.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.681137998045538 R-squared 0.463948972381483 Adjusted R-squared 0.315679539210404 F-TEST (value) 3.12909385608941 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0.00204122686203667 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.271082113454329 Sum Squared Residuals 3.45381907503868 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.155 2.55757335872075 -0.402573358720753 2 2.172 2.49774115418935 -0.325741154189352 3 2.15 2.56773154467335 -0.417731544673346 4 2.533 2.65958346188570 -0.126583461885697 5 2.058 2.22727044662270 -0.169270446622695 6 2.16 2.42862921350386 -0.268629213503857 7 2.26 2.63087922231101 -0.370879222311009 8 2.498 2.45904383476168 0.0389561652383172 9 2.695 2.80053940433388 -0.105539404333883 10 2.799 2.58034562571720 0.218654374282803 11 2.947 2.61642640081375 0.33057359918625 12 2.93 2.86087304497395 0.0691269550260502 13 2.318 2.34111672614333 -0.0231167261433267 14 2.54 2.37208115989020 0.167918840109803 15 2.57 2.34686692618904 0.223133073810957 16 2.669 2.64817688801212 0.0208231119878763 17 2.45 2.28284951572685 0.167150484273151 18 2.842 2.54304702306142 0.29895297693858 19 3.44 2.55925641238813 0.880743587611872 20 2.678 2.53099542294852 0.147004577051475 21 2.981 2.57007167369531 0.41092832630469 22 2.26 2.48920173534957 -0.229201735349573 23 2.844 2.4627442103923 0.381255789607698 24 2.546 2.70416036424152 -0.158160364241524 25 2.456 2.29023506419299 0.165764935807014 26 2.295 2.23040285966159 0.0645971403384149 27 2.379 2.19597908397642 0.183020916023581 28 2.479 2.51692819729532 -0.0379281972953199 29 2.057 2.06804587786450 -0.0110458778645022 30 2.28 2.29282206987595 -0.0128220698759509 31 2.351 2.40935249560115 -0.0583524956011465 32 2.276 2.36810369054307 -0.0921036905430653 33 2.548 2.5537061156765 -0.00570611567649984 34 2.311 2.47968429829323 -0.168684298293233 35 2.201 2.41776610099581 -0.216766100995814 36 2.725 2.69298993247010 0.0320100675298954 37 2.408 2.34054029301570 0.0674597069843029 38 2.139 2.22761547251664 -0.0886154725166388 39 1.898 2.23014793581860 -0.332147935818597 40 2.537 2.43582034626925 0.101179653730753 41 2.069 2.10965320592454 -0.0406532059245358 42 2.063 2.16944478256428 -0.106444782564285 43 2.524 2.54994272148079 -0.0259427214807943 44 2.437 2.29817323235229 0.138826767647711 45 2.189 2.49680283012123 -0.307802830121227 46 2.793 2.37279760111533 0.420202398884668 47 2.074 2.28388049013829 -0.209880490138289 48 2.622 2.59826455355314 0.0237354464468572 49 2.278 2.15316849602026 0.124831503979743 50 2.144 1.96215935374223 0.181840646257774 51 2.427 2.08327450934259 0.343725490657406 52 2.139 2.09649110653761 0.0425088934623879 53 1.828 1.77418095386142 0.0538190461385819 54 2.072 1.98305691099449 0.0889430890055127 55 1.8 2.22556914821892 -0.425569148218922 56 1.758 1.99068381939444 -0.232683819394438 57 2.246 2.23787997617308 0.00812002382691998 58 1.987 2.22797073952466 -0.240970739524665 59 1.868 2.15318279765984 -0.285182797659845 60 2.514 2.48071210476128 0.03328789523872 61 2.121 2.05336606190698 0.0676339380930193 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0915680095592984 0.183136019118597 0.908431990440702 18 0.106753579186263 0.213507158372525 0.893246420813737 19 0.784837701992914 0.430324596014172 0.215162298007086 20 0.761017028457816 0.477965943084368 0.238982971542184 21 0.732336558108436 0.535326883783129 0.267663441891564 22 0.95115056163527 0.0976988767294587 0.0488494383647294 23 0.979481974028564 0.0410360519428713 0.0205180259714357 24 0.985941966154927 0.0281160676901463 0.0140580338450732 25 0.974276238042633 0.0514475239147336 0.0257237619573668 26 0.962978865957737 0.0740422680845252 0.0370211340422626 27 0.943736764607692 0.112526470784616 0.056263235392308 28 0.932188588795973 0.135622822408054 0.0678114112040271 29 0.911738831158343 0.176522337683315 0.0882611688416574 30 0.883281063158495 0.233437873683009 0.116718936841505 31 0.899807379260169 0.200385241479662 0.100192620739831 32 0.874919552354847 0.250160895290306 0.125080447645153 33 0.849768725691866 0.300462548616267 0.150231274308134 34 0.8215577724806 0.356884455038799 0.178442227519399 35 0.828254388976777 0.343491222046447 0.171745611023223 36 0.751528101572132 0.496943796855736 0.248471898427868 37 0.656566869630201 0.686866260739597 0.343433130369799 38 0.601439584260483 0.797120831479033 0.398560415739517 39 0.806417718791877 0.387164562416246 0.193582281208123 40 0.709206738313203 0.581586523373595 0.290793261686797 41 0.631930888689163 0.736138222621673 0.368069111310837 42 0.593366386068655 0.81326722786269 0.406633613931345 43 0.481752713144172 0.963505426288344 0.518247286855828 44 0.478895569839736 0.957791139679471 0.521104430160264 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 2 0.0714285714285714 NOK 10% type I error level 5 0.178571428571429 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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