Seatbelt Law part 1

*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 15:35:54 -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/t1258756602qqfy2og8whzgo7i.htm/, Retrieved Fri, 20 Nov 2009 23:36:54 +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/t1258756602qqfy2og8whzgo7i.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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8.9 1,6 8.8 1,3 8.3 1,1 7.5 1,6 7.2 1,9 7.4 1,6 8.8 1,7 9.3 1,6 9.3 1,4 8.7 2,1 8.2 1,9 8.3 1,7 8.5 1,8 8.6 2 8.5 2,5 8.2 2,1 8.1 2,1 7.9 2,3 8.6 2,4 8.7 2,4 8.7 2,3 8.5 1,7 8.4 2 8.5 2,3 8.7 2 8.7 2 8.6 1,3 8.5 1,7 8.3 1,9 8 1,7 8.2 1,6 8.1 1,7 8.1 1,8 8 1,9 7.9 1,9 7.9 1,9 8 2 8 2,1 7.9 1,9 8 1,9 7.7 1,3 7.2 1,3 7.5 1,4 7.3 1,2 7 1,3 7 1,8 7 2,2 7.2 2,6 7.3 2,8 7.1 3,1 6.8 3,9 6.4 3,7 6.1 4,6 6.5 5,1 7.7 5,2 7.9 4,9 7.5 5,1 6.9 4,8 6.6 3,9 6.9 3,5

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TWIB[t] = + 8.74315783324895 -0.362640679154173GI[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) 8.74315783324895 0.19592 44.6262 0 0 GI -0.362640679154173 0.077072 -4.7052 1.6e-05 8e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.525604291373647 R-squared 0.276259871110393 Adjusted R-squared 0.26378159302609 F-TEST (value) 22.1392622639097 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.61549115280657e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.637776285338418 Sum Squared Residuals 23.5919982281241 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 8.16293274660231 0.737067253397693 2 8.8 8.27172495034853 0.528275049651468 3 8.3 8.34425308617937 -0.0442530861793669 4 7.5 8.16293274660228 -0.662932746602281 5 7.2 8.05414054285603 -0.85414054285603 6 7.4 8.16293274660228 -0.762932746602281 7 8.8 8.12666867868686 0.673331321313136 8 9.3 8.16293274660228 1.13706725339772 9 9.3 8.23546088243312 1.06453911756688 10 8.7 7.9816124070252 0.718387592974804 11 8.2 8.05414054285603 0.145859457143970 12 8.3 8.12666867868686 0.173331321313136 13 8.5 8.09040461077145 0.409595389228553 14 8.6 8.01787647494061 0.582123525059387 15 8.5 7.83655613536353 0.663443864636474 16 8.2 7.9816124070252 0.218387592974804 17 8.1 7.9816124070252 0.118387592974804 18 7.9 7.90908427119436 -0.0090842711943604 19 8.6 7.87282020327894 0.727179796721056 20 8.7 7.87282020327894 0.827179796721056 21 8.7 7.90908427119436 0.790915728805639 22 8.5 8.12666867868686 0.373331321313136 23 8.4 8.01787647494061 0.382123525059388 24 8.5 7.90908427119436 0.590915728805639 25 8.7 8.01787647494061 0.682123525059387 26 8.7 8.01787647494061 0.682123525059387 27 8.6 8.27172495034853 0.328275049651466 28 8.5 8.12666867868686 0.373331321313136 29 8.3 8.05414054285603 0.245859457143971 30 8 8.12666867868686 -0.126668678686864 31 8.2 8.16293274660228 0.0370672533977179 32 8.1 8.12666867868686 -0.0266686786868646 33 8.1 8.09040461077145 0.00959538922855273 34 8 8.05414054285603 -0.0541405428560297 35 7.9 8.05414054285603 -0.154140542856029 36 7.9 8.05414054285603 -0.154140542856029 37 8 8.01787647494061 -0.0178764749406124 38 8 7.9816124070252 0.0183875929748048 39 7.9 8.05414054285603 -0.154140542856029 40 8 8.05414054285603 -0.0541405428560297 41 7.7 8.27172495034853 -0.571724950348533 42 7.2 8.27172495034853 -1.07172495034853 43 7.5 8.23546088243312 -0.735460882433116 44 7.3 8.30798901826395 -1.00798901826395 45 7 8.27172495034853 -1.27172495034853 46 7 8.09040461077145 -1.09040461077145 47 7 7.94534833910978 -0.945348339109778 48 7.2 7.80029206744811 -0.600292067448109 49 7.3 7.72776393161727 -0.427763931617275 50 7.1 7.61897172787102 -0.518971727871023 51 6.8 7.32885918454769 -0.528859184547685 52 6.4 7.40138732037852 -1.00138732037852 53 6.1 7.07501070913976 -0.975010709139765 54 6.5 6.89369036956268 -0.393690369562678 55 7.7 6.85742630164726 0.84257369835274 56 7.9 6.96621850539351 0.933781494606488 57 7.5 6.89369036956268 0.606309630437322 58 6.9 7.00248257330893 -0.102482573308929 59 6.6 7.32885918454769 -0.728859184547685 60 6.9 7.47391545620935 -0.573915456209353 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.692932436607664 0.614135126784673 0.307067563392336 6 0.638400565761958 0.723198868476084 0.361599434238042 7 0.740740036857516 0.518519926284968 0.259259963142484 8 0.872337856034976 0.255324287930048 0.127662143965024 9 0.896463379263541 0.207073241472919 0.103536620736459 10 0.904800331056935 0.190399337886129 0.0951996689430645 11 0.855299451082332 0.289401097835337 0.144700548917668 12 0.794006463019367 0.411987073961266 0.205993536980633 13 0.734819366485455 0.530361267029091 0.265180633514545 14 0.693868388438818 0.612263223122364 0.306131611561182 15 0.655070981280999 0.689858037438002 0.344929018719001 16 0.578903352011614 0.842193295976771 0.421096647988386 17 0.502449091436524 0.995101817126951 0.497550908563476 18 0.432864357769386 0.865728715538773 0.567135642230614 19 0.420422906101712 0.840845812203424 0.579577093898288 20 0.430157240999414 0.860314481998827 0.569842759000586 21 0.43704651902274 0.87409303804548 0.56295348097726 22 0.388034981498437 0.776069962996874 0.611965018501563 23 0.342513023170581 0.685026046341161 0.65748697682942 24 0.326427199921061 0.652854399842122 0.673572800078939 25 0.347794668262691 0.695589336525383 0.652205331737309 26 0.385376133268375 0.770752266536751 0.614623866731625 27 0.378442763479787 0.756885526959573 0.621557236520213 28 0.382526516796448 0.765053033592896 0.617473483203552 29 0.372864680482523 0.745729360965045 0.627135319517477 30 0.349403144372079 0.698806288744157 0.650596855627921 31 0.332039663106753 0.664079326213506 0.667960336893247 32 0.316272602241869 0.632545204483738 0.683727397758131 33 0.308879164341833 0.617758328683667 0.691120835658167 34 0.303153349262321 0.606306698524643 0.696846650737678 35 0.297458010330839 0.594916020661678 0.702541989669161 36 0.294597020363154 0.589194040726308 0.705402979636846 37 0.309147318225818 0.618294636451636 0.690852681774182 38 0.341001849673895 0.68200369934779 0.658998150326105 39 0.370586793808779 0.741173587617557 0.629413206191221 40 0.451269307596974 0.902538615193948 0.548730692403026 41 0.491348218465264 0.982696436930528 0.508651781534736 42 0.527367856067824 0.945264287864352 0.472632143932176 43 0.53703182628797 0.92593634742406 0.46296817371203 44 0.531199136357069 0.937601727285862 0.468800863642931 45 0.528427160284945 0.94314567943011 0.471572839715055 46 0.535500503123751 0.9289989937525 0.46449949687625 47 0.542896704906938 0.914206590186124 0.457103295093062 48 0.538540874531473 0.922918250937053 0.461459125468527 49 0.567319107941826 0.865361784116349 0.432680892058174 50 0.592097989332226 0.815804021335547 0.407902010667773 51 0.507068209512438 0.985863580975123 0.492931790487562 52 0.430467275636982 0.860934551273965 0.569532724363017 53 0.598661057985531 0.802677884028938 0.401338942014469 54 0.818066110407717 0.363867779184566 0.181933889592283 55 0.697474049250068 0.605051901499865 0.302525950749932 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 = 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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