Seatbelt Law Model 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: Mon, 14 Dec 2009 13:15:52 -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/t1260821826o58jjvesdkjzj5s.htm/, Retrieved Mon, 14 Dec 2009 21:17:18 +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/t1260821826o58jjvesdkjzj5s.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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7.2 -6 7.5 8.3 7.4 0 7.2 7.5 8.8 -4 7.4 7.2 9.3 -2 8.8 7.4 9.3 -2 9.3 8.8 8.7 -6 9.3 9.3 8.2 -7 8.7 9.3 8.3 -6 8.2 8.7 8.5 -6 8.3 8.2 8.6 -3 8.5 8.3 8.5 -2 8.6 8.5 8.2 -5 8.5 8.6 8.1 -11 8.2 8.5 7.9 -11 8.1 8.2 8.6 -11 7.9 8.1 8.7 -10 8.6 7.9 8.7 -14 8.7 8.6 8.5 -8 8.7 8.7 8.4 -9 8.5 8.7 8.5 -5 8.4 8.5 8.7 -1 8.5 8.4 8.7 -2 8.7 8.5 8.6 -5 8.7 8.7 8.5 -4 8.6 8.7 8.3 -6 8.5 8.6 8 -2 8.3 8.5 8.2 -2 8 8.3 8.1 -2 8.2 8 8.1 -2 8.1 8.2 8 2 8.1 8.1 7.9 1 8 8.1 7.9 -8 7.9 8 8 -1 7.9 7.9 8 1 8 7.9 7.9 -1 8 8 8 2 7.9 8 7.7 2 8 7.9 7.2 1 7.7 8 7.5 -1 7.2 7.7 7.3 -2 7.5 7.2 7 -2 7.3 7.5 7 -1 7 7.3 7 -8 7 7 7.2 -4 7 7 7.3 -6 7.2 7 7.1 -3 7.3 7.2 6.8 -3 7.1 7.3 6.4 -7 6.8 7.1 6.1 -9 6.4 6.8 6.5 -11 6.1 6.4 7.7 -13 6.5 6.1 7.9 -11 7.7 6.5 7.5 -9 7.9 7.7 6.9 -17 7.5 7.9 6.6 -22 6.9 7.5 6.9 -25 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TW[t] = + 2.75714764262054 -0.00337666443229272CV[t] + 1.32623679314269TW1[t] -0.639603306651212TW2[t] -0.109035744813868M1[t] -0.0460005199250042M2[t] + 0.673083023163224M3[t] -0.271431816286714M4[t] -0.0474155919942077M5[t] -0.0865653868507958M6[t] + 0.0235232511887366M7[t] + 0.246755675487309M8[t] + 0.137257167200593M9[t] -0.00491680202440453M10[t] -0.0173049943056759M11[t] -0.0118920563247720t + 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) 2.75714764262054 0.527471 5.2271 6e-06 3e-06 CV -0.00337666443229272 0.004699 -0.7186 0.476578 0.238289 TW1 1.32623679314269 0.10123 13.1012 0 0 TW2 -0.639603306651212 0.099888 -6.4032 0 0 M1 -0.109035744813868 0.118356 -0.9213 0.36244 0.18122 M2 -0.0460005199250042 0.120025 -0.3833 0.703558 0.351779 M3 0.673083023163224 0.122248 5.5059 2e-06 1e-06 M4 -0.271431816286714 0.145796 -1.8617 0.070002 0.035001 M5 -0.0474155919942077 0.118628 -0.3997 0.691504 0.345752 M6 -0.0865653868507958 0.116184 -0.7451 0.460584 0.230292 M7 0.0235232511887366 0.118638 0.1983 0.843832 0.421916 M8 0.246755675487309 0.119056 2.0726 0.044696 0.022348 M9 0.137257167200593 0.124156 1.1055 0.27554 0.13777 M10 -0.00491680202440453 0.124872 -0.0394 0.968787 0.484394 M11 -0.0173049943056759 0.121992 -0.1419 0.887907 0.443954 t -0.0118920563247720 0.002358 -5.0431 1e-05 5e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.980458370849766 R-squared 0.961298616969377 Adjusted R-squared 0.946785598332893 F-TEST (value) 66.2369863256984 F-TEST (DF numerator) 15 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.171586434098140 Sum Squared Residuals 1.17767617466061 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.2 7.2945483314408 -0.0945483314407923 2 7.4 7.4392431207893 -0.0392431207892947 3 8.8 8.61706961590582 0.182930384094177 4 9.3 9.38272024033606 -0.0827202403360574 5 9.3 9.36251817556344 -0.0625181755634421 6 8.7 9.00518132878565 -0.305181328785649 7 8.2 8.31101249904708 -0.111012499047083 8 8.3 8.23961979000797 0.06038020999203 9 8.5 8.57065455803636 -0.0706545580363608 10 8.6 8.60774556715313 -0.00774556715312895 11 8.5 8.58479167209882 -0.0847916720988191 12 8.2 8.40375059339721 -0.203750593397212 13 8.1 7.96917207157464 0.13082792842536 14 7.9 8.07957255281983 -0.179572552819826 15 8.6 8.58547701161987 0.0145229883801341 16 8.7 8.681979867943 0.0180201320570091 17 8.7 8.59251205829832 0.107487941701683 18 8.5 8.45724988985808 0.0427501101419214 19 8.4 8.2935757773766 0.106424222623407 20 8.5 8.4867064696372 0.0132935303628041 21 8.7 8.54839325727593 0.151606742724072 22 8.7 8.59899092412187 0.101009075878132 23 8.6 8.45692000748246 0.143079992517539 24 8.5 8.3263326017168 0.173667398283198 25 8.3 8.1434947807936 0.156505219206401 26 8 7.9798442636651 0.0201557363348963 27 8.2 8.41708537381599 -0.217085373815993 28 8.1 7.91780682866518 0.182193171334815 29 8.1 7.8693866559884 0.230613344011592 30 8 7.868798477743 0.131201522257002 31 7.9 7.83774804457578 0.0622519554242182 32 7.9 8.01081504379107 -0.110815043791068 33 8 7.92974815881865 0.0702518411813467 34 8 7.90155248371857 0.0984475162814332 35 7.9 7.82006523331199 0.0799347666880124 36 8 7.68272449868174 0.317275501318255 37 7.7 7.75838070752249 -0.0583807075224943 38 7.2 7.35106917191095 -0.151069171910950 39 7.5 7.59377658296301 -0.093776582963008 40 7.3 7.358419042889 -0.0584190428890049 41 7 7.11341486023284 -0.113414860232837 42 7 6.78904596800662 0.210954031993382 43 7 7.10276019274279 -0.102760192742791 44 7.2 7.30059390298742 -0.100593902987420 45 7.3 7.45120402586906 -0.151204025869058 46 7.1 7.29171102500644 -0.191711025006436 47 6.8 6.93822308710673 -0.138223087106733 48 6.4 6.68719230620424 -0.287192306204241 49 6.1 6.23440410866847 -0.134404108668474 50 6.5 6.15027089081483 0.349729109185174 51 7.7 7.58659141569531 0.113408584304690 52 7.9 7.95907402016676 -0.0590740201667619 53 7.5 7.662168249917 -0.162168249916996 54 6.9 6.97972433560666 -0.0797243356066566 55 6.6 6.55490348625775 0.0450965137422496 56 6.9 6.76226479357635 0.137735206423654 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.170836706027506 0.341673412055013 0.829163293972494 20 0.201516690933704 0.403033381867409 0.798483309066295 21 0.150050902050833 0.300101804101666 0.849949097949167 22 0.0759213508774094 0.151842701754819 0.92407864912259 23 0.0492411089202135 0.098482217840427 0.950758891079787 24 0.0515732769993417 0.103146553998683 0.948426723000658 25 0.027211430377822 0.054422860755644 0.972788569622178 26 0.0149208241781074 0.0298416483562148 0.985079175821893 27 0.153612415289636 0.307224830579272 0.846387584710364 28 0.102739990513264 0.205479981026527 0.897260009486736 29 0.0726734931475349 0.14534698629507 0.927326506852465 30 0.0467658089700294 0.0935316179400588 0.95323419102997 31 0.0426857444672038 0.0853714889344075 0.957314255532796 32 0.152186221383871 0.304372442767742 0.847813778616129 33 0.100020984911161 0.200041969822322 0.89997901508884 34 0.0590434017992282 0.118086803598456 0.940956598200772 35 0.0341172747809487 0.0682345495618975 0.965882725219051 36 0.240414379366149 0.480828758732297 0.759585620633851 37 0.752417236451776 0.495165527096448 0.247582763548224 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 1 0.0526315789473684 NOK 10% type I error level 6 0.315789473684211 NOK

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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