Seatbelt Law Model 4

*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 12:44:45 -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/t12608199444vl5odvhkvbjwpc.htm/, Retrieved Mon, 14 Dec 2009 20:45:57 +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/t12608199444vl5odvhkvbjwpc.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 8,8 8,9 7,4 0 7,2 7,5 8,3 8,8 8,8 -4 7,4 7,2 7,5 8,3 9,3 -2 8,8 7,4 7,2 7,5 9,3 -2 9,3 8,8 7,4 7,2 8,7 -6 9,3 9,3 8,8 7,4 8,2 -7 8,7 9,3 9,3 8,8 8,3 -6 8,2 8,7 9,3 9,3 8,5 -6 8,3 8,2 8,7 9,3 8,6 -3 8,5 8,3 8,2 8,7 8,5 -2 8,6 8,5 8,3 8,2 8,2 -5 8,5 8,6 8,5 8,3 8,1 -11 8,2 8,5 8,6 8,5 7,9 -11 8,1 8,2 8,5 8,6 8,6 -11 7,9 8,1 8,2 8,5 8,7 -10 8,6 7,9 8,1 8,2 8,7 -14 8,7 8,6 7,9 8,1 8,5 -8 8,7 8,7 8,6 7,9 8,4 -9 8,5 8,7 8,7 8,6 8,5 -5 8,4 8,5 8,7 8,7 8,7 -1 8,5 8,4 8,5 8,7 8,7 -2 8,7 8,5 8,4 8,5 8,6 -5 8,7 8,7 8,5 8,4 8,5 -4 8,6 8,7 8,7 8,5 8,3 -6 8,5 8,6 8,7 8,7 8 -2 8,3 8,5 8,6 8,7 8,2 -2 8 8,3 8,5 8,6 8,1 -2 8,2 8 8,3 8,5 8,1 -2 8,1 8,2 8 8,3 8 2 8,1 8,1 8,2 8 7,9 1 8 8,1 8,1 8,2 7,9 -8 7,9 8 8,1 8,1 8 -1 7,9 7,9 8 8,1 8 1 8 7,9 7,9 8 7,9 -1 8 8 7,9 7,9 8 2 7,9 8 8 7,9 7,7 2 8 7,9 8 8 7,2 1 7,7 8 7,9 8 7,5 -1 7,2 7,7 8 7,9 7,3 -2 7,5 7,2 7,7 8 7 -2 7,3 7,5 7,2 7,7 7 -1 7 7,3 7,5 7,2 7 -8 7 7 7,3 7,5 7,2 -4 7 7 7 7,3 7,3 -6 7,2 7 7 7 7,1 -3 7,3 7,2 7 7 etc...

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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation TW[t] = + 1.35270011267557 -0.00657570862911655CV[t] + 1.46760231982947TW1[t] -0.781349635612117TW2[t] -0.150146906344660TW3[t] + 0.312242286743154`TW4 `[t] -0.149267397052989M1[t] -0.115804029829894M2[t] + 0.594188677576061M3[t] -0.413818723946786M4[t] -0.0394767830123892M5[t] + 0.088878732353515M6[t] -0.0152657568680250M7[t] + 0.134639932667193M8[t] + 0.0116315590137514M9[t] -0.0929071923986117M10[t] -0.0189529698826592M11[t] -0.00698033699299656t + 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) 1.35270011267557 0.585528 2.3102 0.026401 0.013201 CV -0.00657570862911655 0.004255 -1.5453 0.130566 0.065283 TW1 1.46760231982947 0.137899 10.6426 0 0 TW2 -0.781349635612117 0.265134 -2.947 0.005458 0.002729 TW3 -0.150146906344660 0.267526 -0.5612 0.577927 0.288964 `TW4 ` 0.312242286743154 0.139906 2.2318 0.031603 0.015801 M1 -0.149267397052989 0.103935 -1.4362 0.159137 0.079568 M2 -0.115804029829894 0.106599 -1.0864 0.284165 0.142082 M3 0.594188677576061 0.10943 5.4299 3e-06 2e-06 M4 -0.413818723946786 0.141402 -2.9265 0.005758 0.002879 M5 -0.0394767830123892 0.159351 -0.2477 0.805674 0.402837 M6 0.088878732353515 0.121514 0.7314 0.469005 0.234502 M7 -0.0152657568680250 0.103899 -0.1469 0.883965 0.441982 M8 0.134639932667193 0.107486 1.2526 0.217996 0.108998 M9 0.0116315590137514 0.112751 0.1032 0.918377 0.459189 M10 -0.0929071923986117 0.113715 -0.817 0.41901 0.209505 M11 -0.0189529698826592 0.107729 -0.1759 0.861281 0.430641 t -0.00698033699299656 0.002418 -2.8862 0.006396 0.003198 Multiple Linear Regression - Regression Statistics Multiple R 0.986015428500645 R-squared 0.97222642524131 Adjusted R-squared 0.959801404954528 F-TEST (value) 78.2474718593075 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.149133013777705 Sum Squared Residuals 0.84514492034 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.2 7.21538562972578 -0.0153856297257767 2 7.4 7.43106264522006 -0.0310626452200583 3 8.8 8.65229958650316 0.147700413496839 4 9.3 9.3177839938768 -0.0177839938767922 5 9.3 9.20135520058408 0.098644799415917 6 8.7 8.8106011841335 -0.110601184133507 7 8.2 8.18755642291849 0.0124435770815104 8 8.3 8.21503583165571 0.0849641683442926 9 8.5 8.71257031460507 -0.212570314605074 10 8.6 8.68443768184348 -0.0844376818434823 11 8.5 8.5641903295918 -0.0641903295918009 12 8.2 8.37218974023004 -0.172189740230040 13 8.1 7.94068429228529 0.159315707714712 14 7.9 8.10105090052486 -0.201050900524857 15 8.6 8.60249761376222 -0.00249761376221810 16 8.7 8.68586772223183 0.0141322777681728 17 8.7 8.67815280033877 0.0218471996612257 18 8.5 8.51438747158588 -0.0143874715858782 19 8.4 8.31987280012031 0.0801271998796932 20 8.5 8.47722924195985 0.0227707580401458 21 8.7 8.57586227361004 0.124137726389959 22 8.7 8.63887062752431 0.0611293724756861 23 8.6 8.52306279250342 0.076937207496585 24 8.5 8.3828943321864 0.117105667813602 25 8.3 8.23362120432554 0.0663787956744591 26 8 8.03343059026896 -0.0334305902689587 27 8.2 8.43622265381565 -0.23622265381565 28 8.1 7.94796542254395 0.152034577456049 29 8.1 7.99489248193475 0.105107518065251 30 8 8.04439772206052 -0.0443977220605231 31 7.9 7.87055152047525 0.0294484795247471 32 7.9 7.97280875358347 -0.0728087535834725 33 8 7.8899397367289 0.110060263271103 34 8 7.8958199250084 0.104180074991599 35 7.9 7.86658603555406 0.0334139644459371 36 8 7.69705661993896 0.302943380061036 37 7.7 7.79692831011145 -0.0969283101114518 38 7.2 7.32658608009508 -0.126586080095081 39 7.5 7.49711467922639 0.00288532077360756 40 7.3 7.39592646367228 -0.0959264636722778 41 7 7.21676348011353 -0.216763480113532 42 7 6.84638696575593 0.153613034244069 43 7 7.13939905792072 -0.139399057920724 44 7.2 7.23861719050125 -0.0386171905012457 45 7.3 7.32162767505599 -0.0216276750559888 46 7.1 7.1808717656238 -0.0808717656238027 47 6.8 6.84616084235072 -0.0461608423507212 48 6.4 6.6478593076446 -0.247859307644598 49 6.1 6.21338056355194 -0.113380563551942 50 6.5 6.10786978389104 0.392130216108955 51 7.7 7.61186546669258 0.088134533307422 52 7.9 7.95245639767515 -0.0524563976751523 53 7.5 7.50883603702886 -0.00883603702886197 54 6.9 6.88422665646416 0.0157733435358398 55 6.6 6.58262019856523 0.0173798014347733 56 6.9 6.89630898229972 0.00369101770027978 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0950031305655785 0.190006261131157 0.904996869434421 22 0.165191891261600 0.330383782523201 0.8348081087384 23 0.08341105832629 0.16682211665258 0.91658894167371 24 0.0354965244777141 0.0709930489554282 0.964503475522286 25 0.0666317042918453 0.133263408583691 0.933368295708155 26 0.0371231151660062 0.0742462303320124 0.962876884833994 27 0.228538783629487 0.457077567258973 0.771461216370513 28 0.159654305078609 0.319308610157218 0.840345694921391 29 0.100178231659854 0.200356463319708 0.899821768340146 30 0.0815446049069758 0.163089209813952 0.918455395093024 31 0.0644747470010004 0.128949494002001 0.935525252999 32 0.0571982513285374 0.114396502657075 0.942801748671463 33 0.0324382665405526 0.0648765330811053 0.967561733459447 34 0.0142519915922420 0.0285039831844839 0.985748008407758 35 0.00506901033022194 0.0101380206604439 0.994930989669778 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 2 0.133333333333333 NOK 10% type I error level 5 0.333333333333333 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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