Seatbelt law q3

*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: Thu, 27 Nov 2008 09:42:54 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227804400jx5ptybmg72g4vt.htm/, Retrieved Thu, 27 Nov 2008 16:46:49 +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/27/t1227804400jx5ptybmg72g4vt.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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4,9 1 6,6 1 8 1 7,6 1 9,2 1 10,7 1 11,2 1 10,7 1 10,4 1 10,1 1 11,4 1 11,5 1 12,2 1 11,9 1 12,3 1 12,4 1 13 0 13,2 0 13 0 12,7 0 14,2 0 15,2 0 15 0 14,1 0 14 0 13,8 0 13,3 0 13,1 0 12,7 0 13,5 0 14,3 0 15 0 15 0 14,5 0 13,7 0 13,1 0 13,1 0 13,4 0 12,9 0 12,9 0 12,6 0 12,3 0 12,3 0 12,8 0 15,8 0 16,2 0 15,8 0 15,3 0 14,9 0 14,4 0 13,6 0 13,1 0 13,2 0 12,9 0 13 0 13 0 15,7 0 15,2 0 14,1 0 13,7 0 13,6 0

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 Koers/winst[t] = + 13.3134768211921 -2.93394039735099kredietcrisis[t] -0.919181383370124M1[t] -0.707292126563647M2[t] -0.729884105960267M3[t] -0.952476085356883M4[t] -1.24185614422370M5[t] -0.884448123620311M6[t] -0.667040103016925M7[t] -0.609632082413541M8[t] + 0.747775938189843M9[t] + 0.745183958793227M10[t] + 0.482591979396612M11[t] + 0.0225919793966151t + 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) 13.3134768211921 0.909594 14.6367 0 0 kredietcrisis -2.93394039735099 0.633684 -4.63 2.9e-05 1.5e-05 M1 -0.919181383370124 0.83707 -1.0981 0.277757 0.138879 M2 -0.707292126563647 0.878244 -0.8053 0.424675 0.212337 M3 -0.729884105960267 0.877296 -0.832 0.409633 0.204816 M4 -0.952476085356883 0.876629 -1.0865 0.28279 0.141395 M5 -1.24185614422370 0.879235 -1.4124 0.164412 0.082206 M6 -0.884448123620311 0.8774 -1.008 0.318601 0.1593 M7 -0.667040103016925 0.875845 -0.7616 0.450106 0.225053 M8 -0.609632082413541 0.874571 -0.6971 0.489196 0.244598 M9 0.747775938189843 0.873578 0.856 0.396345 0.198173 M10 0.745183958793227 0.872869 0.8537 0.397591 0.198796 M11 0.482591979396612 0.872443 0.5532 0.582782 0.291391 t 0.0225919793966151 0.015744 1.435 0.157921 0.07896 Multiple Linear Regression - Regression Statistics Multiple R 0.831061812260906 R-squared 0.690663735798381 Adjusted R-squared 0.605102641444742 F-TEST (value) 8.0721704299824 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 3.74107753664532e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.37922812038804 Sum Squared Residuals 89.4066997792492 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.9 9.48294701986753 -4.58294701986754 2 6.6 9.71742825607062 -3.11742825607062 3 8 9.71742825607064 -1.71742825607064 4 7.6 9.51742825607064 -1.91742825607064 5 9.2 9.25064017660044 -0.0506401766004418 6 10.7 9.63064017660044 1.06935982339956 7 11.2 9.87064017660044 1.32935982339956 8 10.7 9.95064017660044 0.749359823399557 9 10.4 11.3306401766004 -0.930640176600441 10 10.1 11.3506401766004 -1.25064017660044 11 11.4 11.1106401766004 0.289359823399559 12 11.5 10.6506401766004 0.849359823399558 13 12.2 9.75405077262694 2.44594922737306 14 11.9 9.98853200883002 1.91146799116998 15 12.3 9.98853200883002 2.31146799116998 16 12.4 9.78853200883002 2.61146799116998 17 13 12.4556843267108 0.544315673289182 18 13.2 12.8356843267108 0.364315673289181 19 13 13.0756843267108 -0.0756843267108186 20 12.7 13.1556843267108 -0.455684326710819 21 14.2 14.5356843267108 -0.335684326710818 22 15.2 14.5556843267108 0.644315673289182 23 15 14.3156843267108 0.684315673289182 24 14.1 13.8556843267108 0.244315673289181 25 14 12.9590949227373 1.04090507726269 26 13.8 13.1935761589404 0.606423841059599 27 13.3 13.1935761589404 0.106423841059602 28 13.1 12.9935761589404 0.106423841059602 29 12.7 12.7267880794702 -0.0267880794701999 30 13.5 13.1067880794702 0.3932119205298 31 14.3 13.3467880794702 0.953211920529801 32 15 13.4267880794702 1.5732119205298 33 15 14.8067880794702 0.193211920529802 34 14.5 14.8267880794702 -0.326788079470198 35 13.7 14.5867880794702 -0.8867880794702 36 13.1 14.1267880794702 -1.0267880794702 37 13.1 13.2301986754967 -0.130198675496692 38 13.4 13.4646799116998 -0.0646799116997822 39 12.9 13.4646799116998 -0.564679911699779 40 12.9 13.2646799116998 -0.364679911699778 41 12.6 12.9978918322296 -0.39789183222958 42 12.3 13.3778918322296 -1.07789183222958 43 12.3 13.6178918322296 -1.31789183222958 44 12.8 13.6978918322296 -0.897891832229579 45 15.8 15.0778918322296 0.722108167770421 46 16.2 15.0978918322296 1.10210816777042 47 15.8 14.8578918322296 0.94210816777042 48 15.3 14.3978918322296 0.90210816777042 49 14.9 13.5013024282561 1.39869757174393 50 14.4 13.7357836644592 0.664216335540837 51 13.6 13.7357836644592 -0.135783664459160 52 13.1 13.5357836644592 -0.43578366445916 53 13.2 13.2689955849890 -0.0689955849889616 54 12.9 13.6489955849890 -0.74899558498896 55 13 13.8889955849890 -0.88899558498896 56 13 13.9689955849890 -0.968995584988961 57 15.7 15.3489955849890 0.351004415011039 58 15.2 15.3689955849890 -0.168995584988961 59 14.1 15.1289955849890 -1.02899558498896 60 13.7 14.6689955849890 -0.968995584988962 61 13.6 13.7724061810155 -0.172406181015454 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.763504115613787 0.472991768772426 0.236495884386213 18 0.695072291650199 0.609855416699603 0.304927708349801 19 0.654935322196871 0.690129355606258 0.345064677803129 20 0.567689157490729 0.864621685018543 0.432310842509271 21 0.587020266803355 0.82595946639329 0.412979733196645 22 0.733280092854989 0.533439814290021 0.266719907145011 23 0.646380773551608 0.707238452896785 0.353619226448392 24 0.556933011932259 0.886133976135482 0.443066988067741 25 0.458808269757634 0.917616539515268 0.541191730242366 26 0.437334513067044 0.874669026134089 0.562665486932955 27 0.606541724200672 0.786916551598657 0.393458275799328 28 0.667922124988914 0.664155750022172 0.332077875011086 29 0.908252827228862 0.183494345542276 0.0917471727711378 30 0.95253183950449 0.0949363209910204 0.0474681604955102 31 0.97227861511406 0.0554427697718789 0.0277213848859395 32 0.992392895424243 0.0152142091515132 0.00760710457575659 33 0.98691921402516 0.0261615719496778 0.0130807859748389 34 0.98406078962814 0.0318784207437192 0.0159392103718596 35 0.987022209378345 0.0259555812433107 0.0129777906216554 36 0.990719782336713 0.0185604353265737 0.00928021766328685 37 0.990326107017035 0.0193477859659309 0.00967389298296546 38 0.987775968368153 0.0244480632636935 0.0122240316318467 39 0.983543724943983 0.0329125501120347 0.0164562750560173 40 0.969461858020257 0.0610762839594857 0.0305381419797428 41 0.9577678740211 0.0844642519578004 0.0422321259789002 42 0.95082453459019 0.0983509308196214 0.0491754654098107 43 0.95944374588378 0.0811125082324406 0.0405562541162203 44 0.954793969986852 0.0904120600262954 0.0452060300131477 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 8 0.285714285714286 NOK 10% type I error level 15 0.535714285714286 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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