paper_seatbelt law

*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: Tue, 15 Dec 2009 15:25:43 -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/15/t1260916049dth1pghebzm4r36.htm/, Retrieved Tue, 15 Dec 2009 23:27:41 +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/15/t1260916049dth1pghebzm4r36.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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17 8 18 8,5 23,8 10,4 25,5 11,1 25,6 10,9 23,7 10 22 9,2 21,3 9,2 20,7 9,5 20,4 9,6 20,3 9,5 20,4 9,1 19,8 8,9 19,5 9 23,1 10,1 23,5 10,3 23,5 10,2 22,9 9,6 21,9 9,2 21,5 9,3 20,5 9,4 20,2 9,4 19,4 9,2 19,2 9 18,8 9 18,8 9 22,6 9,8 23,3 10 23 9,8 21,4 9,3 19,9 9 18,8 9 18,6 9,1 18,4 9,1 18,6 9,1 19,9 9,2 19,2 8,8 18,4 8,3 21,1 8,4 20,5 8,1 19,1 7,7 18,1 7,9 17 7,9 17,1 8 17,4 7,9 16,8 7,6 15,3 7,1 14,3 6,8 13,4 6,5 15,3 6,9 22,1 8,2 23,7 8,7 22,2 8,3 19,5 7,9 16,6 7,5 17,3 7,8 19,8 8,3 21,2 8,4 21,5 8,2 20,6 7,7 19,1 7,2 19,6 7,3 23,5 8,1 24 8,5

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 <25j[t] = + 2.53135016025638 + 2.01338141025641vrouwen[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) 2.53135016025638 1.91735 1.3202 0.19161 0.095805 vrouwen 2.01338141025641 0.217744 9.2466 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.761352903014468 R-squared 0.579658242928558 Adjusted R-squared 0.572878537169342 F-TEST (value) 85.4990265824636 F-TEST (DF numerator) 1 F-TEST (DF denominator) 62 p-value 2.81330514440015e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.72003690073149 Sum Squared Residuals 183.428670272436 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17 18.6384014423078 -1.63840144230777 2 18 19.6450921474359 -1.64509214743590 3 23.8 23.4705168269231 0.329483173076923 4 25.5 24.8798838141026 0.620116185897436 5 25.6 24.4772075320513 1.12279246794872 6 23.7 22.6651642628205 1.03483573717949 7 22 21.0544591346154 0.945540865384618 8 21.3 21.0544591346154 0.245540865384618 9 20.7 21.6584735576923 -0.958473557692308 10 20.4 21.8598116987179 -1.45981169871795 11 20.3 21.6584735576923 -1.35847355769231 12 20.4 20.8531209935897 -0.453120993589744 13 19.8 20.4504447115385 -0.65044471153846 14 19.5 20.6517828525641 -1.15178285256410 15 23.1 22.8665024038462 0.233497596153848 16 23.5 23.2691786858974 0.230821314102563 17 23.5 23.0678405448718 0.432159455128207 18 22.9 21.8598116987179 1.04018830128205 19 21.9 21.0544591346154 0.845540865384616 20 21.5 21.255797275641 0.244202724358974 21 20.5 21.4571354166667 -0.957135416666667 22 20.2 21.4571354166667 -1.25713541666667 23 19.4 21.0544591346154 -1.65445913461538 24 19.2 20.6517828525641 -1.45178285256410 25 18.8 20.6517828525641 -1.8517828525641 26 18.8 20.6517828525641 -1.8517828525641 27 22.6 22.2624879807692 0.33751201923077 28 23.3 22.6651642628205 0.634835737179488 29 23 22.2624879807692 0.737512019230768 30 21.4 21.255797275641 0.144202724358972 31 19.9 20.6517828525641 -0.751782852564103 32 18.8 20.6517828525641 -1.8517828525641 33 18.6 20.8531209935897 -2.25312099358974 34 18.4 20.8531209935897 -2.45312099358974 35 18.6 20.8531209935897 -2.25312099358974 36 19.9 21.0544591346154 -1.15445913461538 37 19.2 20.2491065705128 -1.04910657051282 38 18.4 19.2424158653846 -0.842415865384617 39 21.1 19.4437540064103 1.65624599358975 40 20.5 18.8397395833333 1.66026041666667 41 19.1 18.0343870192308 1.06561298076923 42 18.1 18.4370633012821 -0.337063301282049 43 17 18.4370633012821 -1.43706330128205 44 17.1 18.6384014423077 -1.53840144230769 45 17.4 18.4370633012821 -1.03706330128205 46 16.8 17.8330488782051 -1.03304887820512 47 15.3 16.8263581730769 -1.52635817307692 48 14.3 16.22234375 -1.92234375000000 49 13.4 15.6183293269231 -2.21832932692307 50 15.3 16.4236818910256 -1.12368189102564 51 22.1 19.0410777243590 3.05892227564103 52 23.7 20.0477684294872 3.65223157051282 53 22.2 19.2424158653846 2.95758413461538 54 19.5 18.4370633012821 1.06293669871795 55 16.6 17.6317107371795 -1.03171073717948 56 17.3 18.2357251602564 -0.935725160256407 57 19.8 19.2424158653846 0.557584134615385 58 21.2 19.4437540064103 1.75624599358974 59 21.5 19.0410777243590 2.45892227564103 60 20.6 18.0343870192308 2.56561298076923 61 19.1 17.0276963141026 2.07230368589744 62 19.6 17.2290344551282 2.3709655448718 63 23.5 18.8397395833333 4.66026041666667 64 24 19.6450921474359 4.35490785256410 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00948412009518353 0.0189682401903671 0.990515879904816 6 0.0197415291880838 0.0394830583761675 0.980258470811916 7 0.0420094373933351 0.0840188747866702 0.957990562606665 8 0.0199853037354874 0.0399706074709748 0.980014696264513 9 0.0139260713716378 0.0278521427432755 0.986073928628362 10 0.0177902659076529 0.0355805318153059 0.982209734092347 11 0.0142931310385183 0.0285862620770365 0.985706868961482 12 0.00651441807219377 0.0130288361443875 0.993485581927806 13 0.00282101931629240 0.00564203863258481 0.997178980683708 14 0.00131856278209410 0.00263712556418821 0.998681437217906 15 0.000516870154561723 0.00103374030912345 0.999483129845438 16 0.000194094420842215 0.00038818884168443 0.999805905579158 17 7.23675934513183e-05 0.000144735186902637 0.99992763240655 18 9.43099955391744e-05 0.000188619991078349 0.99990569000446 19 0.000119326810045881 0.000238653620091762 0.999880673189954 20 5.71064388073144e-05 0.000114212877614629 0.999942893561193 21 3.06317862422336e-05 6.12635724844672e-05 0.999969368213758 22 2.23079278418920e-05 4.46158556837841e-05 0.999977692072158 23 2.18875279531627e-05 4.37750559063254e-05 0.999978112472047 24 1.30342739359444e-05 2.60685478718888e-05 0.999986965726064 25 1.23256020098685e-05 2.46512040197369e-05 0.99998767439799 26 1.11403626649718e-05 2.22807253299435e-05 0.999988859637335 27 4.83654417794757e-06 9.67308835589514e-06 0.999995163455822 28 2.15636873834376e-06 4.31273747668751e-06 0.999997843631262 29 1.17674082479012e-06 2.35348164958025e-06 0.999998823259175 30 5.63405645061977e-07 1.12681129012395e-06 0.999999436594355 31 2.19618297612147e-07 4.39236595224294e-07 0.999999780381702 32 2.27431244143772e-07 4.54862488287545e-07 0.999999772568756 33 6.30959652623275e-07 1.26191930524655e-06 0.999999369040347 34 3.14738514122346e-06 6.29477028244693e-06 0.99999685261486 35 1.56040939366387e-05 3.12081878732775e-05 0.999984395906063 36 3.74004668188092e-05 7.48009336376185e-05 0.999962599533181 37 0.000102104170185533 0.000204208340371067 0.999897895829814 38 0.000207680521649300 0.000415361043298599 0.99979231947835 39 0.00208723520810603 0.00417447041621206 0.997912764791894 40 0.00762050915808898 0.0152410183161780 0.99237949084191 41 0.0109151927459026 0.0218303854918053 0.989084807254097 42 0.00882307592486788 0.0176461518497358 0.991176924075132 43 0.0125290019872716 0.0250580039745433 0.987470998012728 44 0.0283884854520806 0.0567769709041612 0.97161151454792 45 0.0439496043299151 0.0878992086598301 0.956050395670085 46 0.0478924792521651 0.0957849585043302 0.952107520747835 47 0.0388755474066891 0.0777510948133782 0.96112445259331 48 0.0297807747300765 0.059561549460153 0.970219225269924 49 0.0220707418993357 0.0441414837986714 0.977929258100664 50 0.0174152296542345 0.0348304593084691 0.982584770345766 51 0.0473510570785246 0.0947021141570493 0.952648942921475 52 0.0901167117248717 0.180233423449743 0.909883288275128 53 0.106056052008486 0.212112104016971 0.893943947991514 54 0.0821500886890331 0.164300177378066 0.917849911310967 55 0.134626966811884 0.269253933623768 0.865373033188116 56 0.391067702200032 0.782135404400065 0.608932297799968 57 0.641497971820492 0.717004056359016 0.358502028179508 58 0.82425650761294 0.35148698477412 0.17574349238706 59 0.923470563586548 0.153058872826904 0.076529436413452 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.490909090909091 NOK 5% type I error level 40 0.727272727272727 NOK 10% type I error level 47 0.854545454545454 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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