*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, 18 Nov 2009 11:51:21 -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/18/t1258570351wukqw6zd42uj3cw.htm/, Retrieved Wed, 18 Nov 2009 19:52:43 +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/18/t1258570351wukqw6zd42uj3cw.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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2863.36 99.9 100.1 100.7 101.1 101.2 2897.06 99.7 99.9 100.1 100.7 101.1 3012.61 99.5 99.7 99.9 100.1 100.7 3142.95 99.2 99.5 99.7 99.9 100.1 3032.93 99 99.2 99.5 99.7 99.9 3045.78 99 99 99.2 99.5 99.7 3110.52 99.3 99 99 99.2 99.5 3013.24 99.5 99.3 99 99 99.2 2987.10 99.7 99.5 99.3 99 99 2995.55 100 99.7 99.5 99.3 99 2833.18 100.4 100 99.7 99.5 99.3 2848.96 100.6 100.4 100 99.7 99.5 2794.83 100.7 100.6 100.4 100 99.7 2845.26 100.7 100.7 100.6 100.4 100 2915.02 100.6 100.7 100.7 100.6 100.4 2892.63 100.5 100.6 100.7 100.7 100.6 2604.42 100.6 100.5 100.6 100.7 100.7 2641.65 100.5 100.6 100.5 100.6 100.7 2659.81 100.4 100.5 100.6 100.5 100.6 2638.53 100.3 100.4 100.5 100.6 100.5 2720.25 100.4 100.3 100.4 100.5 100.6 2745.88 100.4 100.4 100.3 100.4 100.5 2735.7 100.4 100.4 100.4 100.3 100.4 2811.7 100.4 100.4 100.4 100.4 100.3 2799.43 100.4 100.4 100.4 100.4 100.4 2555.28 100.5 100.4 100.4 100.4 100.4 2304.98 100.6 100.5 100.4 100.4 100.4 2214.95 100.6 100.6 100.5 100.4 100.4 2065.81 1 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 G.indx[t] = + 9.00524964939543 + 3.79035267848712e-05Bel20[t] + 2.05758680536144Y1[t] -1.65019256489537Y2[t] + 0.666098296679429Y3[t] -0.165203885369296Y4[t] + 0.00662830373229754t + 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) 9.00524964939543 3.882542 2.3194 0.024583 0.012292 Bel20 3.79035267848712e-05 6e-05 0.6275 0.533238 0.266619 Y1 2.05758680536144 0.140968 14.5961 0 0 Y2 -1.65019256489537 0.314024 -5.255 3e-06 2e-06 Y3 0.666098296679429 0.317312 2.0992 0.040975 0.020487 Y4 -0.165203885369296 0.144246 -1.1453 0.25765 0.128825 t 0.00662830373229754 0.002495 2.6566 0.010625 0.005312 Multiple Linear Regression - Regression Statistics Multiple R 0.993572100402516 R-squared 0.987185518698267 Adjusted R-squared 0.985616398538871 F-TEST (value) 629.13315642975 F-TEST (DF numerator) 6 F-TEST (DF denominator) 49 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.146643848096271 Sum Squared Residuals 1.05371649103963 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.9 99.5343619222163 0.365638077783737 2 99.7 99.8709468225314 -0.170946822531342 3 99.5 99.4668986068304 0.0331013931695523 4 99.2 99.3628910800364 -0.162891080036366 5 99 98.9779328268604 0.0220671731395807 6 99 98.9684097170462 0.0315902829538136 7 99.3 99.1407416961517 0.159258303848349 8 99.5 99.6773002926816 -0.177300292681640 9 99.7 99.6324381669013 0.067561833098675 10 100 99.920695092532 0.079304907468001 11 100.4 100.292065022975 0.107934977025322 12 100.6 100.727447279298 -0.127447279297661 13 100.7 100.650252912169 0.0497470878308407 14 100.7 100.751391011375 -0.0513910113753113 15 100.6 100.662782313835 -0.0627823138347382 16 100.5 100.496372329660 0.00362767033975323 17 100.6 100.434816645354 0.165183354645630 18 100.5 100.747024204747 -0.247024204746573 19 100.4 100.333473458369 0.066526541631389 20 100.3 100.381685969209 -0.081685969209198 21 100.4 100.267542106899 0.132457893101155 22 100.4 100.595830373917 -0.195830373917341 23 100.4 100.386964122126 0.0130358778736025 24 100.4 100.479603312099 -0.0796033120992248 25 100.4 100.469246151021 -0.069246151020941 26 100.5 100.466620308689 0.033379691311282 27 100.6 100.669520040203 -0.0695200402028997 28 100.6 100.713475313465 -0.11347531346536 29 100.5 100.616041258391 -0.116041258391368 30 100.5 100.462250252742 0.0377497472581364 31 100.7 100.621225011431 0.0787749885693103 32 101.1 100.970993405113 0.129006594886629 33 101.5 101.485297711287 0.0147022887126028 34 101.9 101.781246243511 0.118753756488621 35 102.1 102.179278689254 -0.0792786892535808 36 102.1 102.145216434527 -0.0452164345270023 37 102.1 102.025082940402 0.0749170595979964 38 102.4 102.100715718981 0.299284281018664 39 102.8 102.691955669269 0.108044330730787 40 103.1 103.030040848472 0.069959151528439 41 103.1 103.194913222962 -0.0949132229619776 42 102.9 102.924400466921 -0.0244004669205389 43 102.4 102.655294005754 -0.255294005754493 44 101.9 101.914446196328 -0.0144461963278918 45 101.3 101.589984250629 -0.289984250628655 46 100.7 100.890552498066 -0.190552498066444 47 100.6 100.401098921382 0.198901078617602 48 101 100.877459317507 0.12254068249349 49 101.5 101.569133264105 -0.0691332641052293 50 101.9 101.978772669943 -0.078772669943136 51 102.1 102.26605009441 -0.166050094410077 52 102.3 102.292973544047 0.00702645595290673 53 102.5 102.570520213119 -0.0705202131185575 54 102.9 102.729977310029 0.170022689971441 55 103.6 103.333287160451 0.266712839548725 56 104.3 104.223063581768 0.0769364182315131 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.702581003369348 0.594837993261305 0.297418996630652 11 0.64789942465166 0.70420115069668 0.35210057534834 12 0.650584170446124 0.698831659107752 0.349415829553876 13 0.559554737911873 0.880890524176253 0.440445262088127 14 0.434941976689588 0.869883953379176 0.565058023310412 15 0.331249424963227 0.662498849926454 0.668750575036773 16 0.237122133536696 0.474244267073392 0.762877866463304 17 0.198872174433279 0.397744348866559 0.80112782556672 18 0.296890468737080 0.593780937474160 0.70310953126292 19 0.244356474154153 0.488712948308305 0.755643525845847 20 0.220928154351575 0.44185630870315 0.779071845648425 21 0.285788240801615 0.571576481603229 0.714211759198385 22 0.257221199373260 0.514442398746519 0.74277880062674 23 0.208389545121853 0.416779090243707 0.791610454878147 24 0.150148142455869 0.300296284911739 0.849851857544131 25 0.104593793665914 0.209187587331828 0.895406206334086 26 0.0728244242706859 0.145648848541372 0.927175575729314 27 0.066085745854436 0.132171491708872 0.933914254145564 28 0.0734886140412632 0.146977228082526 0.926511385958737 29 0.0966070855230602 0.193214171046120 0.90339291447694 30 0.0641051668798556 0.128210333759711 0.935894833120144 31 0.0591391366628846 0.118278273325769 0.940860863337115 32 0.0832593107087825 0.166518621417565 0.916740689291218 33 0.104206845144150 0.208413690288301 0.89579315485585 34 0.0765772146659347 0.153154429331869 0.923422785334065 35 0.0575967718339768 0.115193543667954 0.942403228166023 36 0.044084638289159 0.088169276578318 0.95591536171084 37 0.0291374304403327 0.0582748608806655 0.970862569559667 38 0.101944197647396 0.203888395294791 0.898055802352604 39 0.107329128475830 0.214658256951661 0.89267087152417 40 0.103682494416905 0.207364988833810 0.896317505583095 41 0.08312447682204 0.16624895364408 0.91687552317796 42 0.241607425053252 0.483214850106504 0.758392574946748 43 0.313705720149965 0.62741144029993 0.686294279850035 44 0.629630926714327 0.740738146571346 0.370369073285673 45 0.664510213651368 0.670979572697263 0.335489786348632 46 0.645328486621879 0.709343026756242 0.354671513378121 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 2 0.0540540540540541 OK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 2 ; 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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