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Seatbelt Case: Q3

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 06:13:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/21/t1195650476dl20b1lscn6k1vs.htm/, Retrieved Wed, 21 Nov 2007 14:08:06 +0100

User-defined keywords:

Jeroen Goetschalckx, Nick Vandewalle, Jef Jacobs, Nick Van Hove, Michiel Van den Broeck

Dataseries X:

» Textbox « » Textfile « » CSV «

3.926 0 3.517 0 4.142 0 4.353 0 5.029 0 4.755 0 3.862 0 4.406 0 4.567 0 4.863 0 4.121 0 3.626 0 3.804 0 3.491 0 4.151 0 4.254 0 4.717 0 4.866 0 4.001 0 3.758 0 4.78 0 5.016 0 4.296 0 4.467 0 3.891 1 3.872 1 3.867 1 3.973 1 4.64 1 4.538 1 3.836 1 3.77 1 4.374 1 4.497 1 3.945 1 3.862 1 3.608 1 3.301 1 3.882 1 3.605 1 4.305 1 4.216 1 3.971 1 3.988 1 4.317 1 4.484 1 4.247 1 3.52 1 3.687 1 3.405 1 3.99 1 4.047 1 4.549 1 4.559 1 3.926 1 4.206 1 4.517 1 4.387 1 3.219 1 3.129 1

Text written by user:

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 compuational 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 Ongevallen[t] = + 3.88783333333333 -0.278388888888889Superboete[t] + 0.0623999999999995M1[t] -0.203600000000000M2[t] + 0.2856M3[t] + 0.325599999999999M4[t] + 0.9272M5[t] + 0.866M6[t] + 0.198400000000001M7[t] + 0.304800000000000M8[t] + 0.7902M9[t] + 0.9286M10[t] + 0.2448M11[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) 3.88783333333333 0.111386 34.9042 0 0 Superboete -0.278388888888889 0.061881 -4.4988 4.5e-05 2.2e-05 M1 0.0623999999999995 0.148515 0.4202 0.676283 0.338141 M2 -0.203600000000000 0.148515 -1.3709 0.176915 0.088457 M3 0.2856 0.148515 1.923 0.060545 0.030273 M4 0.325599999999999 0.148515 2.1924 0.033339 0.01667 M5 0.9272 0.148515 6.2432 0 0 M6 0.866 0.148515 5.8311 0 0 M7 0.198400000000001 0.148515 1.3359 0.188016 0.094008 M8 0.304800000000000 0.148515 2.0523 0.045731 0.022865 M9 0.7902 0.148515 5.3207 3e-06 1e-06 M10 0.9286 0.148515 6.2526 0 0 M11 0.2448 0.148515 1.6483 0.105956 0.052978 Multiple Linear Regression - Regression Statistics Multiple R 0.885383827025225 R-squared 0.783904521157833 Adjusted R-squared 0.728731207410897 F-TEST (value) 14.2080376892599 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 7.83861864306346e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.234822188149419 Sum Squared Residuals 2.59164862222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.926 3.95023333333333 -0.0242333333333342 2 3.517 3.68423333333333 -0.167233333333334 3 4.142 4.17343333333333 -0.031433333333333 4 4.353 4.21343333333333 0.139566666666667 5 5.029 4.81503333333333 0.213966666666667 6 4.755 4.75383333333333 0.00116666666666764 7 3.862 4.08623333333333 -0.224233333333333 8 4.406 4.19263333333333 0.213366666666666 9 4.567 4.67803333333333 -0.111033333333334 10 4.863 4.81643333333333 0.0465666666666665 11 4.121 4.13263333333333 -0.0116333333333341 12 3.626 3.88783333333333 -0.261833333333332 13 3.804 3.95023333333333 -0.146233333333333 14 3.491 3.68423333333333 -0.193233333333333 15 4.151 4.17343333333333 -0.0224333333333337 16 4.254 4.21343333333333 0.0405666666666664 17 4.717 4.81503333333333 -0.0980333333333334 18 4.866 4.75383333333333 0.112166666666666 19 4.001 4.08623333333333 -0.0852333333333333 20 3.758 4.19263333333333 -0.434633333333333 21 4.78 4.67803333333333 0.101966666666667 22 5.016 4.81643333333333 0.199566666666667 23 4.296 4.13263333333333 0.163366666666667 24 4.467 3.88783333333333 0.579166666666666 25 3.891 3.67184444444444 0.219155555555556 26 3.872 3.40584444444444 0.466155555555556 27 3.867 3.89504444444444 -0.0280444444444448 28 3.973 3.93504444444444 0.0379555555555555 29 4.64 4.53664444444444 0.103355555555555 30 4.538 4.47544444444444 0.0625555555555555 31 3.836 3.80784444444445 0.0281555555555550 32 3.77 3.91424444444444 -0.144244444444444 33 4.374 4.39964444444444 -0.0256444444444447 34 4.497 4.53804444444444 -0.0410444444444445 35 3.945 3.85424444444444 0.0907555555555555 36 3.862 3.60944444444444 0.252555555555556 37 3.608 3.67184444444444 -0.0638444444444441 38 3.301 3.40584444444444 -0.104844444444444 39 3.882 3.89504444444444 -0.0130444444444446 40 3.605 3.93504444444444 -0.330044444444444 41 4.305 4.53664444444444 -0.231644444444445 42 4.216 4.47544444444444 -0.259444444444444 43 3.971 3.80784444444444 0.163155555555555 44 3.988 3.91424444444444 0.0737555555555555 45 4.317 4.39964444444444 -0.0826444444444441 46 4.484 4.53804444444444 -0.0540444444444444 47 4.247 3.85424444444444 0.392755555555556 48 3.52 3.60944444444444 -0.0894444444444444 49 3.687 3.67184444444444 0.0151555555555556 50 3.405 3.40584444444444 -0.000844444444444653 51 3.99 3.89504444444444 0.0949555555555554 52 4.047 3.93504444444444 0.111955555555555 53 4.549 4.53664444444444 0.0123555555555559 54 4.559 4.47544444444445 0.0835555555555553 55 3.926 3.80784444444445 0.118155555555555 56 4.206 3.91424444444444 0.291755555555556 57 4.517 4.39964444444444 0.117355555555556 58 4.387 4.53804444444444 -0.151044444444445 59 3.219 3.85424444444444 -0.635244444444445 60 3.129 3.60944444444444 -0.480444444444444

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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Software written by Ed van Stee & Patrick Wessa

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