Seatbelt Law part 5

*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 15:45:12 -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/t1258757141eugrz1zxw18e077.htm/, Retrieved Fri, 20 Nov 2009 23:45:53 +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/t1258757141eugrz1zxw18e077.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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7.2 1,9 7.5 8.3 7.4 1,6 7.2 7.5 8.8 1,7 7.4 7.2 9.3 1,6 8.8 7.4 9.3 1,4 9.3 8.8 8.7 2,1 9.3 9.3 8.2 1,9 8.7 9.3 8.3 1,7 8.2 8.7 8.5 1,8 8.3 8.2 8.6 2 8.5 8.3 8.5 2,5 8.6 8.5 8.2 2,1 8.5 8.6 8.1 2,1 8.2 8.5 7.9 2,3 8.1 8.2 8.6 2,4 7.9 8.1 8.7 2,4 8.6 7.9 8.7 2,3 8.7 8.6 8.5 1,7 8.7 8.7 8.4 2 8.5 8.7 8.5 2,3 8.4 8.5 8.7 2 8.5 8.4 8.7 2 8.7 8.5 8.6 1,3 8.7 8.7 8.5 1,7 8.6 8.7 8.3 1,9 8.5 8.6 8 1,7 8.3 8.5 8.2 1,6 8 8.3 8.1 1,7 8.2 8 8.1 1,8 8.1 8.2 8 1,9 8.1 8.1 7.9 1,9 8 8.1 7.9 1,9 7.9 8 8 2 7.9 7.9 8 2,1 8 7.9 7.9 1,9 8 8 8 1,9 7.9 8 7.7 1,3 8 7.9 7.2 1,3 7.7 8 7.5 1,4 7.2 7.7 7.3 1,2 7.5 7.2 7 1,3 7.3 7.5 7 1,8 7 7.3 7 2,2 7 7 7.2 2,6 7 7 7.3 2,8 7.2 7 7.1 3,1 7.3 7.2 6.8 3,9 7.1 7.3 6.4 3,7 6.8 7.1 6.1 4,6 6.4 6.8 6.5 5,1 6.1 6.4 7.7 5,2 6.5 6.1 7.9 4,9 7.7 6.5 7.5 5,1 7.9 7.7 6.9 4,8 7.5 7.9 6.6 3,9 6.9 7.5 6.9 3,5 6.6 6.9

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 TWIB[t] = + 2.82378101219517 -0.00508086181364818GI[t] + 1.32411297292159TWIB1[t] -0.64390045548293TWIB2[t] -0.0999061494232035M1[t] -0.0434877570194206M2[t] + 0.679808204282157M3[t] -0.266939596683318M4[t] -0.0382867494972436M5[t] -0.0765162377199005M6[t] + 0.0417633025188104M7[t] + 0.265115558769458M8[t] + 0.136208857605767M9[t] -0.0106577324371968M10[t] -0.0188635725354176M11[t] -0.0115981810749348t + 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) 2.82378101219517 0.558775 5.0535 1e-05 5e-06 GI -0.00508086181364818 0.029186 -0.1741 0.862678 0.431339 TWIB1 1.32411297292159 0.102341 12.9383 0 0 TWIB2 -0.64390045548293 0.104332 -6.1716 0 0 M1 -0.0999061494232035 0.118572 -0.8426 0.404474 0.202237 M2 -0.0434877570194206 0.120697 -0.3603 0.720515 0.360257 M3 0.679808204282157 0.122643 5.543 2e-06 1e-06 M4 -0.266939596683318 0.147656 -1.8078 0.078154 0.039077 M5 -0.0382867494972436 0.118652 -0.3227 0.748617 0.374308 M6 -0.0765162377199005 0.116339 -0.6577 0.514497 0.257249 M7 0.0417633025188104 0.116731 0.3578 0.722393 0.361197 M8 0.265115558769458 0.116836 2.2691 0.028726 0.014363 M9 0.136208857605767 0.125326 1.0868 0.283615 0.141807 M10 -0.0106577324371968 0.125573 -0.0849 0.932786 0.466393 M11 -0.0188635725354176 0.122711 -0.1537 0.8786 0.4393 t -0.0115981810749348 0.002468 -4.6995 3.1e-05 1.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.980218702324364 R-squared 0.96082870438646 Adjusted R-squared 0.946139468531384 F-TEST (value) 65.4103939691571 F-TEST (DF numerator) 15 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.172624993167688 Sum Squared Residuals 1.19197553064577 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.2 7.28909656065474 -0.0890965606547376 2 7.4 7.45332750303755 -0.0533275030375519 3 8.8 8.62250992831203 0.177490071687974 4 9.3 9.38965010344663 -0.0896501034466272 5 9.3 9.36831679070519 -0.0683167907051918 6 8.7 8.99298229039658 -0.292982290396583 7 8.2 8.30621203817013 -0.106212038170130 8 8.3 8.24326607253753 0.056733927462467 9 8.5 8.55661462915117 -0.0566146291511691 10 8.6 8.59756623470657 0.00243376529343414 11 8.5 8.57885298882216 -0.078852988822159 12 8.2 8.39134938216765 -0.19134938216765 13 8.1 7.94700120534132 0.152998794658675 14 7.9 8.05156408366016 -0.151564083660164 15 8.6 8.56232122866942 0.0376787713305824 16 8.7 8.6596344187707 0.0403655812292921 17 8.7 8.55887814951732 0.141121850482679 18 8.5 8.44770895175962 0.0522910482403754 19 8.4 8.28804345779499 0.111956542205012 20 8.5 8.49464206823103 0.00535793176896607 21 8.7 8.55246278737695 0.147537212623046 22 8.7 8.59443056529508 0.105569434704919 23 8.6 8.4494030562949 0.150596943705106 24 8.5 8.32222480573776 0.177775194262242 25 8.3 8.14168305113302 0.158316948866977 26 8 7.98708688578858 0.0129131142114237 27 8.2 8.43083895141669 -0.230838951416692 28 8.1 7.92997761442411 0.170022385575887 29 8.1 7.88533280596514 0.214667194034856 30 8 7.89938709603448 0.100612903965520 31 7.9 7.8736571579061 0.0263428420939034 32 7.9 8.01738998133794 -0.117389981337944 33 8 7.94076705846625 0.0592329415337546 34 8 7.91420549845914 0.0857945015408585 35 7.9 7.83102760410042 0.0689723958995777 36 8 7.70588169826875 0.294118301731254 37 7.7 7.79422722769925 -0.0942272276992488 38 7.2 7.37742350160333 -0.177423501603326 39 7.5 7.61972684583269 -0.119726845832687 40 7.3 7.38158115577295 -0.0815811557729485 41 7 7.14013500447353 -0.140135004473526 42 7 6.81931310348922 0.180686896510782 43 7 7.11713225457241 -0.117132254572414 44 7.2 7.32685398502267 -0.126853985022668 45 7.3 7.45015552500563 -0.150155525005631 46 7.1 7.29379770153921 -0.193797701539212 47 6.8 6.94071635078252 -0.140716350782525 48 6.4 6.68054411382585 -0.280544113825845 49 6.1 6.22799195517167 -0.127991955171666 50 6.5 6.13059802591038 0.369401974089618 51 7.7 7.56460304576918 0.135396954230822 52 7.9 7.9391567075856 -0.0391567075856032 53 7.5 7.64733724933882 -0.147337249338817 54 6.9 6.94060855832010 -0.0406085583200948 55 6.6 6.51495509155637 0.0850449084436289 56 6.9 6.71784789287082 0.182152107129178 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.125089573354652 0.250179146709304 0.874910426645348 20 0.110664218631085 0.221328437262171 0.889335781368915 21 0.0517514508312928 0.103502901662586 0.948248549168707 22 0.0235045655458441 0.0470091310916883 0.976495434454156 23 0.0109720238087526 0.0219440476175052 0.989027976191247 24 0.00886499696052881 0.0177299939210576 0.991135003039471 25 0.00452822379201262 0.00905644758402524 0.995471776207987 26 0.00179681099701878 0.00359362199403755 0.998203189002981 27 0.085789998449837 0.171579996899674 0.914210001550163 28 0.0492997936502471 0.0985995873004942 0.950700206349753 29 0.0454866731818224 0.0909733463636448 0.954513326818178 30 0.0287221985528417 0.0574443971056834 0.971277801447158 31 0.0279640038131412 0.0559280076262823 0.97203599618686 32 0.0526198730358525 0.105239746071705 0.947380126964148 33 0.0298528430185823 0.0597056860371647 0.970147156981418 34 0.0173382138586087 0.0346764277172175 0.982661786141391 35 0.0106223744790231 0.0212447489580462 0.989377625520977 36 0.343795565276888 0.687591130553777 0.656204434723112 37 0.817747413324613 0.364505173350775 0.182252586675388 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.105263157894737 NOK 5% type I error level 7 0.368421052631579 NOK 10% type I error level 12 0.631578947368421 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 = 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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