Q3_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: Sun, 23 Nov 2008 11:49:23 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t122746620340rpkv70yxs4cqd.htm/, Retrieved Sun, 23 Nov 2008 18:50:14 +0000

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/2008/Nov/23/t122746620340rpkv70yxs4cqd.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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127059 0 122860 0 117702 0 113537 0 108366 0 111078 0 150739 1 159129 0 157928 0 147768 0 137507 0 136919 0 136151 0 133001 0 125554 0 119647 0 114158 0 116193 0 152803 1 161761 0 160942 0 149470 0 139208 0 134588 0 130322 0 126611 0 122401 0 117352 0 112135 0 112879 0 148729 1 157230 0 157221 0 146681 0 136524 0 132111 0 125326 0 122716 0 116615 0 113719 0 110737 0 112093 0 143565 1 149946 0 149147 0 134339 0 122683 0 115614 0 116566 0 111272 0 104609 0 101802 0 94542 0 93051 0 124129 1 130374 0 123946 0 114971 0 105531 0 104919 0

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 X[t] = + 141817.102380952 + 21159.6Y[t] -2723.10334821429Q1[t] -6988.5355654762Q2[t] -7448.5677827381Q3[t] -372.101116071428t + 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) 141817.102380952 5728.18448 24.7578 0 0 Y 21159.6 8916.626946 2.373 0.021231 0.010616 Q1 -2723.10334821429 5955.602983 -0.4572 0.649337 0.324669 Q2 -6988.5355654762 5949.39168 -1.1747 0.245283 0.122642 Q3 -7448.5677827381 6647.173856 -1.1206 0.267433 0.133717 t -372.101116071428 121.61047 -3.0598 0.003445 0.001723 Multiple Linear Regression - Regression Statistics Multiple R 0.483434411284219 R-squared 0.233708830013720 Adjusted R-squared 0.162755943903879 F-TEST (value) 3.2938593879313 F-TEST (DF numerator) 5 F-TEST (DF denominator) 54 p-value 0.0114354385753951 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16279.4590509691 Sum Squared Residuals 14311122497.5777 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 127059 138721.897916667 -11662.8979166667 2 122860 134084.364583333 -11224.3645833334 3 117702 133252.23125 -15550.2312500000 4 113537 140328.697916667 -26791.6979166667 5 108366 137233.493452381 -28867.4934523809 6 111078 132595.960119048 -21517.9601190476 7 150739 152923.426785714 -2184.42678571428 8 159129 138840.293452381 20288.7065476191 9 157928 135745.088988095 22182.9110119048 10 147768 131107.555654762 16660.4443452381 11 137507 130275.422321429 7231.57767857144 12 136919 137351.888988095 -432.888988095244 13 136151 134256.684523810 1894.31547619049 14 133001 129619.151190476 3381.84880952382 15 125554 128787.017857143 -3233.01785714285 16 119647 135863.484523810 -16216.4845238095 17 114158 132768.280059524 -18610.2800595238 18 116193 128130.746726190 -11937.7467261905 19 152803 148458.213392857 4344.78660714286 20 161761 134375.080059524 27385.9199404762 21 160942 131279.875595238 29662.1244047619 22 149470 126642.342261905 22827.6577380952 23 139208 125810.208928571 13397.7910714286 24 134588 132886.675595238 1701.3244047619 25 130322 129791.471130952 530.528869047629 26 126611 125153.937797619 1457.06220238096 27 122401 124321.804464286 -1920.80446428571 28 117352 131398.271130952 -14046.2711309524 29 112135 128303.066666667 -16168.0666666667 30 112879 123665.533333333 -10786.5333333333 31 148729 143993 4736 32 157230 129909.866666667 27320.1333333333 33 157221 126814.662202381 30406.3377976190 34 146681 122177.128869048 24503.8711309524 35 136524 121344.995535714 15179.0044642857 36 132111 128421.462202381 3689.53779761904 37 125326 125326.257738095 -0.257738095230707 38 122716 120688.724404762 2027.27559523810 39 116615 119856.591071429 -3241.59107142857 40 113719 126933.057738095 -13214.0577380952 41 110737 123837.853273810 -13100.8532738095 42 112093 119200.319940476 -7107.31994047618 43 143565 139527.786607143 4037.21339285715 44 149946 125444.653273810 24501.3467261905 45 149147 122349.448809524 26797.5511904762 46 134339 117711.915476190 16627.0845238095 47 122683 116879.782142857 5803.21785714286 48 115614 123956.248809524 -8342.24880952382 49 116566 120861.044345238 -4295.04434523809 50 111272 116223.511011905 -4951.51101190476 51 104609 115391.377678571 -10782.3776785714 52 101802 122467.844345238 -20665.8443452381 53 94542 119372.639880952 -24830.6398809524 54 93051 114735.106547619 -21684.1065476190 55 124129 135062.573214286 -10933.5732142857 56 130374 120979.439880952 9394.5601190476 57 123946 117884.235416667 6061.76458333334 58 114971 113246.702083333 1724.29791666667 59 105531 112414.56875 -6883.56875 60 104919 119491.035416667 -14572.0354166667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.91581287338329 0.168374253233421 0.0841871266167103 10 0.847535633097499 0.304928733805002 0.152464366902501 11 0.773751432806001 0.452497134387998 0.226248567193999 12 0.750546624612011 0.498906750775978 0.249453375387989 13 0.711856602871806 0.576286794256388 0.288143397128194 14 0.642028992097434 0.715942015805132 0.357971007902566 15 0.603817105362246 0.792365789275507 0.396182894637754 16 0.708812845551442 0.582374308897116 0.291187154448558 17 0.803223298265335 0.39355340346933 0.196776701734665 18 0.812882306054436 0.374235387891129 0.187117693945564 19 0.748117468131053 0.503765063737895 0.251882531868947 20 0.789332194279646 0.421335611440709 0.210667805720355 21 0.822867639608608 0.354264720782784 0.177132360391392 22 0.796256716488822 0.407486567022355 0.203743283511178 23 0.734589082261188 0.530821835477624 0.265410917738812 24 0.694351072023857 0.611297855952285 0.305648927976142 25 0.654939882000674 0.690120235998651 0.345060117999326 26 0.603088660643573 0.793822678712854 0.396911339356427 27 0.565544834533638 0.868910330932724 0.434455165466362 28 0.651794390261958 0.696411219476085 0.348205609738042 29 0.761437401960906 0.477125196078189 0.238562598039094 30 0.807525935463254 0.384948129073492 0.192474064536746 31 0.75398129279254 0.49203741441492 0.24601870720746 32 0.763884193947125 0.47223161210575 0.236115806052875 33 0.804236295991096 0.391527408017807 0.195763704008903 34 0.802984551301651 0.394030897396697 0.197015448698349 35 0.759706727892242 0.480586544215517 0.240293272107758 36 0.698461779561786 0.603076440876429 0.301538220438214 37 0.638197250320506 0.723605499358989 0.361802749679494 38 0.564316130505699 0.871367738988602 0.435683869494301 39 0.505522193010385 0.988955613979229 0.494477806989615 40 0.545330737800322 0.909338524399356 0.454669262199678 41 0.610806871396075 0.77838625720785 0.389193128603925 42 0.606809832993263 0.786380334013474 0.393190167006737 43 0.511645202504614 0.976709594990772 0.488354797495386 44 0.528861369736745 0.94227726052651 0.471138630263255 45 0.650639331785976 0.698721336428048 0.349360668214024 46 0.706058005554811 0.587883988890377 0.293941994445189 47 0.686112849352628 0.627774301294745 0.313887150647372 48 0.596760298522033 0.806479402955933 0.403239701477967 49 0.51136829578354 0.97726340843292 0.48863170421646 50 0.438854837209425 0.87770967441885 0.561145162790575 51 0.341626789072659 0.683253578145318 0.658373210927341 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 0 0 OK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly 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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