Q3 - Bob Leysen - 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: Sat, 22 Nov 2008 08:47:21 -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/22/t12273688786b8o7qnfksphvoh.htm/, Retrieved Sat, 22 Nov 2008 15:48:07 +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/22/t12273688786b8o7qnfksphvoh.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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Original text written by user:

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User-defined keywords:

Dataseries X:

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15107 0 15024 0 12083 0 15761 0 16943 0 15070 0 13660 0 14769 0 14725 0 15998 0 15371 0 14957 0 15470 0 15102 0 11704 0 16284 0 16727 0 14969 0 14861 0 14583 0 15306 0 17904 0 16379 0 15420 0 17871 0 15913 0 13867 0 17823 0 17872 0 17422 0 16705 0 15991 0 16584 0 19124 0 17839 0 17209 0 18587 0 16258 0 15142 1 19202 1 17747 1 19090 1 18040 1 17516 1 17752 1 21073 1 17170 1 19440 1 19795 1 17575 1 16165 1 19465 1 19932 1 19961 1 17343 1 18924 1 18574 1 21351 1 18595 1 19823 1 20844 1 19640 1 17735 1 19814 1 22239 1 20682 1 17819 1 21872 1 22117 1 21866 1

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation x[t] = + 15874.7894736842 + 3322.17927631579y[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) 15874.7894736842 273.565719 58.0292 0 0 y 3322.17927631579 404.609155 8.2108 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.705585174947096 R-squared 0.497850439105124 Adjusted R-squared 0.490465886739023 F-TEST (value) 67.4178222894746 F-TEST (DF numerator) 1 F-TEST (DF denominator) 68 p-value 9.07429686947125e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1686.37234778114 Sum Squared Residuals 193381915.284540 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15107 15874.7894736842 -767.789473684233 2 15024 15874.7894736842 -850.789473684208 3 12083 15874.7894736842 -3791.78947368421 4 15761 15874.7894736842 -113.78947368421 5 16943 15874.7894736842 1068.21052631579 6 15070 15874.7894736842 -804.78947368421 7 13660 15874.7894736842 -2214.78947368421 8 14769 15874.7894736842 -1105.78947368421 9 14725 15874.7894736842 -1149.78947368421 10 15998 15874.7894736842 123.21052631579 11 15371 15874.7894736842 -503.78947368421 12 14957 15874.7894736842 -917.78947368421 13 15470 15874.7894736842 -404.78947368421 14 15102 15874.7894736842 -772.78947368421 15 11704 15874.7894736842 -4170.78947368421 16 16284 15874.7894736842 409.21052631579 17 16727 15874.7894736842 852.21052631579 18 14969 15874.7894736842 -905.78947368421 19 14861 15874.7894736842 -1013.78947368421 20 14583 15874.7894736842 -1291.78947368421 21 15306 15874.7894736842 -568.78947368421 22 17904 15874.7894736842 2029.21052631579 23 16379 15874.7894736842 504.21052631579 24 15420 15874.7894736842 -454.78947368421 25 17871 15874.7894736842 1996.21052631579 26 15913 15874.7894736842 38.21052631579 27 13867 15874.7894736842 -2007.78947368421 28 17823 15874.7894736842 1948.21052631579 29 17872 15874.7894736842 1997.21052631579 30 17422 15874.7894736842 1547.21052631579 31 16705 15874.7894736842 830.21052631579 32 15991 15874.7894736842 116.21052631579 33 16584 15874.7894736842 709.21052631579 34 19124 15874.7894736842 3249.21052631579 35 17839 15874.7894736842 1964.21052631579 36 17209 15874.7894736842 1334.21052631579 37 18587 15874.7894736842 2712.21052631579 38 16258 15874.7894736842 383.21052631579 39 15142 19196.96875 -4054.96875 40 19202 19196.96875 5.03124999999999 41 17747 19196.96875 -1449.96875 42 19090 19196.96875 -106.96875 43 18040 19196.96875 -1156.96875 44 17516 19196.96875 -1680.96875 45 17752 19196.96875 -1444.96875 46 21073 19196.96875 1876.03125 47 17170 19196.96875 -2026.96875 48 19440 19196.96875 243.03125 49 19795 19196.96875 598.03125 50 17575 19196.96875 -1621.96875 51 16165 19196.96875 -3031.96875 52 19465 19196.96875 268.03125 53 19932 19196.96875 735.03125 54 19961 19196.96875 764.03125 55 17343 19196.96875 -1853.96875 56 18924 19196.96875 -272.96875 57 18574 19196.96875 -622.96875 58 21351 19196.96875 2154.03125 59 18595 19196.96875 -601.96875 60 19823 19196.96875 626.03125 61 20844 19196.96875 1647.03125 62 19640 19196.96875 443.03125 63 17735 19196.96875 -1461.96875 64 19814 19196.96875 617.03125 65 22239 19196.96875 3042.03125 66 20682 19196.96875 1485.03125 67 17819 19196.96875 -1377.96875 68 21872 19196.96875 2675.03125 69 22117 19196.96875 2920.03125 70 21866 19196.96875 2669.03125 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.786277072473963 0.427445855052074 0.213722927526037 6 0.654187745801299 0.691624508397401 0.345812254198701 7 0.59720879331254 0.805582413374919 0.402791206687459 8 0.471680442331428 0.943360884662855 0.528319557668572 9 0.357593655879511 0.715187311759022 0.642406344120489 10 0.301797543809127 0.603595087618254 0.698202456190873 11 0.219285354702743 0.438570709405487 0.780714645297257 12 0.151746735078070 0.303493470156140 0.84825326492193 13 0.104264648814751 0.208529297629501 0.89573535118525 14 0.0675477025740961 0.135095405148192 0.932452297425904 15 0.323621858421508 0.647243716843015 0.676378141578492 16 0.303548093070492 0.607096186140984 0.696451906929508 17 0.310984517173329 0.621969034346659 0.68901548282667 18 0.254316246756142 0.508632493512283 0.745683753243858 19 0.208936642626254 0.417873285252508 0.791063357373746 20 0.180474258089845 0.360948516179691 0.819525741910155 21 0.145120784804916 0.290241569609833 0.854879215195084 22 0.249021703438788 0.498043406877576 0.750978296561212 23 0.220554640595346 0.441109281190692 0.779445359404654 24 0.182732410079663 0.365464820159326 0.817267589920337 25 0.248974299293184 0.497948598586368 0.751025700706816 26 0.207564002817269 0.415128005634538 0.792435997182731 27 0.267900609352849 0.535801218705698 0.732099390647151 28 0.316738250641883 0.633476501283766 0.683261749358117 29 0.356142398663212 0.712284797326424 0.643857601336788 30 0.350003299033029 0.700006598066058 0.649996700966971 31 0.309965591688272 0.619931183376544 0.690034408311728 32 0.272215261161476 0.544430522322953 0.727784738838524 33 0.239541090274291 0.479082180548583 0.760458909725709 34 0.355720495867717 0.711440991735434 0.644279504132283 35 0.348348721954439 0.696697443908879 0.651651278045561 36 0.309254912083133 0.618509824166266 0.690745087916867 37 0.359002788577366 0.718005577154731 0.640997211422634 38 0.296933541940835 0.59386708388167 0.703066458059165 39 0.435694546985358 0.871389093970717 0.564305453014642 40 0.457143458588396 0.914286917176791 0.542856541411604 41 0.425798123402293 0.851596246804586 0.574201876597707 42 0.380500308345331 0.761000616690663 0.619499691654669 43 0.339754616672767 0.679509233345534 0.660245383327233 44 0.328127692101916 0.656255384203832 0.671872307898084 45 0.308989304188177 0.617978608376353 0.691010695811823 46 0.359804375518828 0.719608751037655 0.640195624481172 47 0.391720291777563 0.783440583555126 0.608279708222437 48 0.335279790716326 0.670559581432651 0.664720209283674 49 0.285628291285926 0.571256582571853 0.714371708714074 50 0.292776490406246 0.585552980812491 0.707223509593754 51 0.518491133779145 0.96301773244171 0.481508866220855 52 0.454810684769806 0.909621369539612 0.545189315230194 53 0.39322571149437 0.78645142298874 0.60677428850563 54 0.330567483472591 0.661134966945181 0.66943251652741 55 0.424621904819967 0.849243809639934 0.575378095180033 56 0.379324720123456 0.758649440246911 0.620675279876544 57 0.367978420462145 0.73595684092429 0.632021579537855 58 0.354756903928590 0.709513807857181 0.64524309607141 59 0.34495413292325 0.6899082658465 0.65504586707675 60 0.270382748991867 0.540765497983733 0.729617251008133 61 0.208744041254114 0.417488082508228 0.791255958745886 62 0.149873022999989 0.299746045999977 0.850126977000011 63 0.28344077442719 0.56688154885438 0.71655922557281 64 0.221552220922811 0.443104441845621 0.77844777907719 65 0.186305358380289 0.372610716760578 0.813694641619711 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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