Seatbelt law - Q3(1)

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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 01:39:11 -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/t1227775195a8kiima25n48961.htm/, Retrieved Thu, 27 Nov 2008 08:40:04 +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/t1227775195a8kiima25n48961.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

101.2 0 100.5 0 98 0 106.6 0 90.1 0 96.9 0 125.9 0 112 0 100 0 123.9 0 79.8 0 83.4 0 113.6 0 112.9 0 104 0 109.9 0 99 0 106.3 0 128.9 0 111.1 0 102.9 0 130 0 87 0 87.5 0 117.6 0 103.4 0 110.8 0 112.6 0 102.5 0 112.4 0 135.6 0 105.1 0 127.7 0 137 0 91 0 90.5 0 122.4 1 123.3 1 124.3 1 120 1 118.1 1 119 1 142.7 1 123.6 1 129.6 1 151.6 1 110.4 1 99.2 1 130.5 1 136.2 1 129.7 1 128 1 121.6 1 135.8 1 143.8 1 147.5 1 136.2 1 156.6 1 123.3 1 100.4 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 107.155555555556 + 20.9194444444444x[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) 107.155555555556 2.413277 44.4025 0 0 x 20.9194444444444 3.815726 5.4824 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.584239602789588 R-squared 0.341335913467735 Adjusted R-squared 0.329979636113731 F-TEST (value) 30.0570250996353 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 9.54988062407125e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 14.4796610558116 Sum Squared Residuals 12160.3138888889 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.2 107.155555555556 -5.95555555555551 2 100.5 107.155555555556 -6.65555555555558 3 98 107.155555555556 -9.15555555555556 4 106.6 107.155555555556 -0.555555555555562 5 90.1 107.155555555556 -17.0555555555556 6 96.9 107.155555555556 -10.2555555555556 7 125.9 107.155555555556 18.7444444444445 8 112 107.155555555556 4.84444444444444 9 100 107.155555555556 -7.15555555555556 10 123.9 107.155555555556 16.7444444444445 11 79.8 107.155555555556 -27.3555555555556 12 83.4 107.155555555556 -23.7555555555555 13 113.6 107.155555555556 6.44444444444444 14 112.9 107.155555555556 5.74444444444445 15 104 107.155555555556 -3.15555555555556 16 109.9 107.155555555556 2.74444444444445 17 99 107.155555555556 -8.15555555555556 18 106.3 107.155555555556 -0.85555555555556 19 128.9 107.155555555556 21.7444444444445 20 111.1 107.155555555556 3.94444444444444 21 102.9 107.155555555556 -4.25555555555555 22 130 107.155555555556 22.8444444444444 23 87 107.155555555556 -20.1555555555556 24 87.5 107.155555555556 -19.6555555555556 25 117.6 107.155555555556 10.4444444444444 26 103.4 107.155555555556 -3.75555555555555 27 110.8 107.155555555556 3.64444444444444 28 112.6 107.155555555556 5.44444444444444 29 102.5 107.155555555556 -4.65555555555556 30 112.4 107.155555555556 5.24444444444445 31 135.6 107.155555555556 28.4444444444444 32 105.1 107.155555555556 -2.05555555555556 33 127.7 107.155555555556 20.5444444444444 34 137 107.155555555556 29.8444444444444 35 91 107.155555555556 -16.1555555555556 36 90.5 107.155555555556 -16.6555555555556 37 122.4 128.075 -5.67499999999999 38 123.3 128.075 -4.775 39 124.3 128.075 -3.775 40 120 128.075 -8.075 41 118.1 128.075 -9.975 42 119 128.075 -9.075 43 142.7 128.075 14.625 44 123.6 128.075 -4.4750 45 129.6 128.075 1.52500000000000 46 151.6 128.075 23.525 47 110.4 128.075 -17.675 48 99.2 128.075 -28.875 49 130.5 128.075 2.425 50 136.2 128.075 8.12499999999999 51 129.7 128.075 1.62499999999999 52 128 128.075 -0.0749999999999982 53 121.6 128.075 -6.475 54 135.8 128.075 7.72500000000001 55 143.8 128.075 15.725 56 147.5 128.075 19.425 57 136.2 128.075 8.12499999999999 58 156.6 128.075 28.525 59 123.3 128.075 -4.775 60 100.4 128.075 -27.675 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.117407129698914 0.234814259397828 0.882592870301086 6 0.0465719633506518 0.0931439267013037 0.953428036649348 7 0.377544966484289 0.755089932968578 0.622455033515711 8 0.296367727404739 0.592735454809479 0.70363227259526 9 0.202344186564644 0.404688373129289 0.797655813435356 10 0.296027850880095 0.59205570176019 0.703972149119905 11 0.511237080819933 0.977525838360135 0.488762919180067 12 0.601068111686596 0.797863776626808 0.398931888313404 13 0.5532127029296 0.8935745941408 0.4467872970704 14 0.494105278061438 0.988210556122875 0.505894721938562 15 0.40473806832499 0.80947613664998 0.59526193167501 16 0.33203793658701 0.66407587317402 0.66796206341299 17 0.270400871922896 0.540801743845792 0.729599128077104 18 0.205721053443078 0.411442106886156 0.794278946556922 19 0.325566937072603 0.651133874145206 0.674433062927397 20 0.262636099621058 0.525272199242116 0.737363900378942 21 0.204067541297500 0.408135082595000 0.7959324587025 22 0.309786982190969 0.619573964381938 0.690213017809031 23 0.374530120061808 0.749060240123616 0.625469879938192 24 0.441062426168532 0.882124852337065 0.558937573831467 25 0.404527108288676 0.809054216577351 0.595472891711324 26 0.341505669262437 0.683011338524875 0.658494330737563 27 0.279630174672456 0.559260349344912 0.720369825327544 28 0.226940088267305 0.453880176534609 0.773059911732695 29 0.185766772694693 0.371533545389387 0.814233227305307 30 0.144778666765023 0.289557333530045 0.855221333234977 31 0.272485810483494 0.544971620966987 0.727514189516506 32 0.216883777120254 0.433767554240507 0.783116222879746 33 0.262559984771628 0.525119969543256 0.737440015228372 34 0.582211696340951 0.835576607318097 0.417788303659049 35 0.546747662120232 0.906504675759536 0.453252337879768 36 0.508653574711595 0.98269285057681 0.491346425288405 37 0.437463175235826 0.874926350471652 0.562536824764174 38 0.366323394966178 0.732646789932356 0.633676605033822 39 0.297693945204908 0.595387890409816 0.702306054795092 40 0.246301430550692 0.492602861101385 0.753698569449308 41 0.208093156201223 0.416186312402447 0.791906843798777 42 0.171511566971616 0.343023133943231 0.828488433028384 43 0.174260911055167 0.348521822110335 0.825739088944833 44 0.129632084353725 0.259264168707450 0.870367915646275 45 0.0905994641702846 0.181198928340569 0.909400535829715 46 0.142572873710728 0.285145747421456 0.857427126289272 47 0.159929942182961 0.319859884365921 0.84007005781704 48 0.390810836592360 0.781621673184719 0.60918916340764 49 0.301613327965352 0.603226655930704 0.698386672034648 50 0.228466920147862 0.456933840295725 0.771533079852138 51 0.156717991924991 0.313435983849983 0.843282008075009 52 0.101406489232252 0.202812978464505 0.898593510767748 53 0.0747497432195163 0.149499486439033 0.925250256780484 54 0.040220080883035 0.08044016176607 0.959779919116965 55 0.0245944143878911 0.0491888287757823 0.975405585612109 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 1 0.0196078431372549 OK 10% type I error level 3 0.0588235294117647 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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