Seatbelt Law Model 3

*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: Mon, 14 Dec 2009 12:30:45 -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/14/t1260819138ibf6wmf1b2edenh.htm/, Retrieved Mon, 14 Dec 2009 20:32:30 +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/14/t1260819138ibf6wmf1b2edenh.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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8,9 -3 8,8 -1 8,3 -3 7,5 -4 7,2 -6 7,4 0 8,8 -4 9,3 -2 9,3 -2 8,7 -6 8,2 -7 8,3 -6 8,5 -6 8,6 -3 8,5 -2 8,2 -5 8,1 -11 7,9 -11 8,6 -11 8,7 -10 8,7 -14 8,5 -8 8,4 -9 8,5 -5 8,7 -1 8,7 -2 8,6 -5 8,5 -4 8,3 -6 8 -2 8,2 -2 8,1 -2 8,1 -2 8 2 7,9 1 7,9 -8 8 -1 8 1 7,9 -1 8 2 7,7 2 7,2 1 7,5 -1 7,3 -2 7 -2 7 -1 7 -8 7,2 -4 7,3 -6 7,1 -3 6,8 -3 6,4 -7 6,1 -9 6,5 -11 7,7 -13 7,9 -11 7,5 -9 6,9 -17 6,6 -22 6,9 -25

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 TW[t] = + 8.94088917186533 + 0.00653226645769947CV[t] + 0.137834015945990M1[t] + 0.117136475596342M2[t] -0.0639642653802124M3[t] -0.327677912939847M4[t] -0.520939934167162M5[t] -0.579024567933734M6[t] + 0.222487597672791M7[t] + 0.348322323780837M8[t] + 0.241995769638123M9[t] -0.0256372377961309M10[t] -0.174979899148826M11[t] -0.0310605392742062t + 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) 8.94088917186533 0.259467 34.4587 0 0 CV 0.00653226645769947 0.012606 0.5182 0.6068 0.3034 M1 0.137834015945990 0.304449 0.4527 0.652869 0.326434 M2 0.117136475596342 0.310165 0.3777 0.707421 0.353711 M3 -0.0639642653802124 0.305866 -0.2091 0.835274 0.417637 M4 -0.327677912939847 0.303316 -1.0803 0.285632 0.142816 M5 -0.520939934167162 0.297755 -1.7496 0.086863 0.043432 M6 -0.579024567933734 0.300481 -1.927 0.06017 0.030085 M7 0.222487597672791 0.297156 0.7487 0.457836 0.228918 M8 0.348322323780837 0.298584 1.1666 0.249393 0.124696 M9 0.241995769638123 0.297781 0.8127 0.420597 0.210298 M10 -0.0256372377961309 0.297434 -0.0862 0.931686 0.465843 M11 -0.174979899148826 0.294236 -0.5947 0.554964 0.277482 t -0.0310605392742062 0.003651 -8.5073 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.833530486242842 R-squared 0.694773071496228 Adjusted R-squared 0.608513287353858 F-TEST (value) 8.05442627064214 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.60466417218086e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.465075588310465 Sum Squared Residuals 9.94958393074696 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 9.02806584916405 -0.128065849164049 2 8.8 8.98937230245557 -0.189372302455567 3 8.3 8.76414648928941 -0.464146489289408 4 7.5 8.46284003599787 -0.962840035997868 5 7.2 8.22545294258095 -1.02545294258095 6 7.4 8.17550136828637 -0.775501368286366 7 8.8 8.91982392878789 -0.119823928787886 8 9.3 9.02766264853713 0.272337351462873 9 9.3 8.8902755551202 0.409724444879795 10 8.7 8.56545294258095 0.134547057419051 11 8.2 8.37851747549635 -0.178517475496348 12 8.3 8.52896910182867 -0.228969101828666 13 8.5 8.63574257850045 -0.13574257850045 14 8.6 8.6035812982497 -0.00358129824969552 15 8.5 8.39795228445663 0.102047715543366 16 8.2 8.0835812982497 0.116418701750304 17 8.1 7.82006513900198 0.279934860998023 18 7.9 7.7309199659612 0.169080034038802 19 8.6 8.50137159229352 0.0986284077064826 20 8.7 8.60267804558506 0.0973219544149426 21 8.7 8.43916188633734 0.260838113662661 22 8.5 8.17966193837507 0.320338061624925 23 8.4 7.99272647129047 0.407273528709526 24 8.5 8.1627748969959 0.337225103004108 25 8.7 8.29567743949847 0.404322560501526 26 8.7 8.23738709341692 0.462612906583079 27 8.6 8.00562901379306 0.594370986206939 28 8.5 7.71738709341692 0.78261290658308 29 8.3 7.48 0.82 30 8 7.41698389279002 0.583016107209981 31 8.2 8.18743551912234 0.0125644808776612 32 8.1 8.28220970595618 -0.182209705956178 33 8.1 8.14482261253926 -0.0448226125392585 34 8 7.8722581316616 0.127741868338404 35 7.9 7.685322664577 0.214677335423006 36 7.9 7.77045162633232 0.129548373667681 37 8 7.922950968208 0.0770490317920008 38 8 7.88425742149954 0.115742578500455 39 7.9 7.65903160833339 0.240968391666616 40 8 7.38385422087264 0.616145779127357 41 7.7 7.15953166037112 0.540468339628879 42 7.2 7.06385422087264 0.136145779127357 43 7.5 7.82124131428956 -0.321241314289563 44 7.3 7.9094832346657 -0.609483234665704 45 7 7.77209614124878 -0.772096141248784 46 7 7.47993486099802 -0.479934860998023 47 7 7.25380579516723 -0.253805795167225 48 7.2 7.42385422087264 -0.223854220872643 49 7.3 7.51756316462903 -0.217563164629028 50 7.1 7.48540188437827 -0.385401884378273 51 6.8 7.27324060412751 -0.473240604127512 52 6.4 6.95233735146287 -0.552337351462873 53 6.1 6.71495025804595 -0.614950258045954 54 6.5 6.61274055208978 -0.112740552089775 55 7.7 7.3701276455067 0.329872354493305 56 7.9 7.47796636525593 0.422033634744066 57 7.5 7.35364380475441 0.146356195245586 58 6.9 7.00269212638436 -0.102692126384357 59 6.6 6.78962759346896 -0.189627593468958 60 6.9 6.91395015397048 -0.0139501539704796 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.748587726766066 0.502824546467869 0.251412273233934 18 0.630818150412371 0.738363699175257 0.369181849587629 19 0.622420647568670 0.755158704862659 0.377579352431330 20 0.705011536367549 0.589976927264903 0.294988463632451 21 0.670549968066885 0.65890006386623 0.329450031933115 22 0.595437049294871 0.809125901410258 0.404562950705129 23 0.487537318197841 0.975074636395681 0.512462681802159 24 0.378404117526084 0.756808235052168 0.621595882473916 25 0.303875048680921 0.607750097361842 0.696124951319079 26 0.219740706883745 0.439481413767489 0.780259293116256 27 0.15278213261779 0.30556426523558 0.84721786738221 28 0.140786632464107 0.281573264928215 0.859213367535893 29 0.116465026568124 0.232930053136248 0.883534973431876 30 0.0769502921529257 0.153900584305851 0.923049707847074 31 0.127279613939020 0.254559227878039 0.87272038606098 32 0.243058285593693 0.486116571187386 0.756941714406307 33 0.278982996917883 0.557965993835765 0.721017003082117 34 0.220637529394565 0.44127505878913 0.779362470605435 35 0.166349589367778 0.332699178735557 0.833650410632222 36 0.127370846657695 0.254741693315391 0.872629153342305 37 0.0950310084178322 0.190062016835664 0.904968991582168 38 0.0667758914682906 0.133551782936581 0.93322410853171 39 0.0495559243322247 0.0991118486644494 0.950444075667775 40 0.130855254165295 0.261710508330590 0.869144745834705 41 0.696254298964743 0.607491402070515 0.303745701035257 42 0.921772576933837 0.156454846132326 0.0782274230661632 43 0.836249988886449 0.327500022227102 0.163750011113551 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 1 0.0370370370370370 OK

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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