CASE: Seatbelt Law Q3

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 23 Nov 2008 07:05:03 -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/23/t1227449197h749z1u0nerledl.htm/, Retrieved Sun, 23 Nov 2008 14:06:37 +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/23/t1227449197h749z1u0nerledl.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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IsPrivate?

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User-defined keywords:

Dataseries X:

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8,4 0 8,4 0 8,6 0 8,9 0 8,8 0 8,3 0 7,5 0 7,2 0 7,5 0 8,8 0 9,3 0 9,3 0 8,7 0 8,2 0 8,3 0 8,5 0 8,6 0 8,6 0 8,2 0 8,1 0 8 0 8,6 0 8,7 0 8,8 0 8,5 1 8,4 1 8,5 1 8,7 1 8,7 1 8,6 1 8,5 1 8,3 1 8,1 1 8,2 1 8,1 1 8,1 1 7,9 1 7,9 1 7,9 1 8 1 8 1 7,9 1 8 1 7,7 1 7,2 1 7,5 1 7,3 1 7 1 7 1 7 1 7,2 1 7,3 1 7,1 1 6,8 1 6,6 1 6,2 1 6,2 1 6,8 1 6,9 1 6,8 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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Werkloosheidsgraad[t] = + 9.40833333333333 + 0.761111111111111y[t] -0.469861111111114M1[t] -0.538055555555556M2[t] -0.36625M3[t] -0.134444444444445M4[t] -0.122638888888889M5[t] -0.270833333333333M6[t] -0.499027777777778M7[t] -0.707222222222222M8[t] -0.755416666666667M9[t] -0.123611111111111M10[t] + 0.00819444444444408M11[t] -0.0518055555555555t + 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) 9.40833333333333 0.236016 39.8631 0 0 y 0.761111111111111 0.227107 3.3513 0.001615 0.000807 M1 -0.469861111111114 0.281908 -1.6667 0.102366 0.051183 M2 -0.538055555555556 0.280303 -1.9196 0.06113 0.030565 M3 -0.36625 0.278842 -1.3135 0.19554 0.09777 M4 -0.134444444444445 0.277529 -0.4844 0.630377 0.315188 M5 -0.122638888888889 0.276365 -0.4438 0.659299 0.329649 M6 -0.270833333333333 0.275352 -0.9836 0.330463 0.165232 M7 -0.499027777777778 0.274492 -1.818 0.075579 0.03779 M8 -0.707222222222222 0.273787 -2.5831 0.013036 0.006518 M9 -0.755416666666667 0.273237 -2.7647 0.008171 0.004085 M10 -0.123611111111111 0.272843 -0.453 0.652644 0.326322 M11 0.00819444444444408 0.272607 0.0301 0.97615 0.488075 t -0.0518055555555555 0.006556 -7.902 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.861862270776383 R-squared 0.742806573787824 Adjusted R-squared 0.670121475075687 F-TEST (value) 10.2195166127468 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.26703780800597e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.430904564795214 Sum Squared Residuals 8.54122222222223 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.4 8.88666666666668 -0.486666666666676 2 8.4 8.76666666666667 -0.366666666666666 3 8.6 8.88666666666667 -0.286666666666667 4 8.9 9.06666666666667 -0.166666666666666 5 8.8 9.02666666666667 -0.226666666666665 6 8.3 8.82666666666667 -0.526666666666666 7 7.5 8.54666666666667 -1.04666666666667 8 7.2 8.28666666666667 -1.08666666666667 9 7.5 8.18666666666667 -0.686666666666666 10 8.8 8.76666666666667 0.0333333333333344 11 9.3 8.84666666666667 0.453333333333334 12 9.3 8.78666666666667 0.513333333333334 13 8.7 8.265 0.435000000000002 14 8.2 8.145 0.0549999999999991 15 8.3 8.265 0.0350000000000007 16 8.5 8.445 0.0550000000000002 17 8.6 8.405 0.195000000000000 18 8.6 8.205 0.395 19 8.2 7.925 0.275000000000000 20 8.1 7.665 0.434999999999999 21 8 7.565 0.435 22 8.6 8.145 0.455 23 8.7 8.225 0.475 24 8.8 8.165 0.635 25 8.5 8.40444444444444 0.095555555555558 26 8.4 8.28444444444444 0.115555555555556 27 8.5 8.40444444444445 0.0955555555555552 28 8.7 8.58444444444444 0.115555555555555 29 8.7 8.54444444444444 0.155555555555555 30 8.6 8.34444444444444 0.255555555555555 31 8.5 8.06444444444444 0.435555555555556 32 8.3 7.80444444444444 0.495555555555556 33 8.1 7.70444444444444 0.395555555555555 34 8.2 8.28444444444444 -0.084444444444445 35 8.1 8.36444444444444 -0.264444444444445 36 8.1 8.30444444444444 -0.204444444444445 37 7.9 7.78277777777778 0.117222222222225 38 7.9 7.66277777777778 0.237222222222223 39 7.9 7.78277777777778 0.117222222222222 40 8 7.96277777777778 0.0372222222222221 41 8 7.92277777777778 0.077222222222222 42 7.9 7.72277777777778 0.177222222222222 43 8 7.44277777777778 0.557222222222222 44 7.7 7.18277777777778 0.517222222222222 45 7.2 7.08277777777778 0.117222222222222 46 7.5 7.66277777777778 -0.162777777777778 47 7.3 7.74277777777778 -0.442777777777778 48 7 7.68277777777778 -0.682777777777778 49 7 7.16111111111111 -0.161111111111109 50 7 7.04111111111111 -0.0411111111111112 51 7.2 7.16111111111111 0.0388888888888886 52 7.3 7.34111111111111 -0.0411111111111115 53 7.1 7.30111111111111 -0.201111111111111 54 6.8 7.10111111111111 -0.301111111111112 55 6.6 6.82111111111111 -0.221111111111112 56 6.2 6.56111111111111 -0.361111111111111 57 6.2 6.46111111111111 -0.261111111111111 58 6.8 7.04111111111111 -0.241111111111111 59 6.9 7.12111111111111 -0.221111111111111 60 6.8 7.06111111111111 -0.261111111111112 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.563241674284762 0.873516651430477 0.436758325715238 18 0.621969098230835 0.75606180353833 0.378030901769165 19 0.902016426445473 0.195967147109055 0.0979835735545273 20 0.980681528195573 0.0386369436088533 0.0193184718044267 21 0.982109170260043 0.0357816594799151 0.0178908297399575 22 0.978525718899054 0.042948562201892 0.021474281100946 23 0.98740990788042 0.0251801842391596 0.0125900921195798 24 0.986118041528616 0.0277639169427685 0.0138819584713843 25 0.974959988944755 0.0500800221104897 0.0250400110552449 26 0.963257109740756 0.0734857805184887 0.0367428902592443 27 0.948295543392264 0.103408913215472 0.0517044566077358 28 0.921896731571188 0.156206536857624 0.0781032684288119 29 0.879500536817036 0.240998926365927 0.120499463182964 30 0.823416947394498 0.353166105211005 0.176583052605502 31 0.828872705010407 0.342254589979186 0.171127294989593 32 0.813148521280723 0.373702957438554 0.186851478719277 33 0.755001777073613 0.489996445852774 0.244998222926387 34 0.776571379911784 0.446857240176431 0.223428620088215 35 0.858437774725118 0.283124450549763 0.141562225274882 36 0.87216200662305 0.255675986753899 0.127837993376949 37 0.83184965622414 0.336300687551718 0.168150343775859 38 0.754622426271013 0.490755147457975 0.245377573728987 39 0.673861890218997 0.652276219562005 0.326138109781003 40 0.587452528552861 0.825094942894278 0.412547471447139 41 0.467416954727544 0.934833909455088 0.532583045272456 42 0.346720530659526 0.693441061319051 0.653279469340474 43 0.325412713171907 0.650825426343814 0.674587286828093 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 5 0.185185185185185 NOK 10% type I error level 7 0.259259259259259 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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