Q3 Seatbelt law zonder dummies en trends

*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: Mon, 24 Nov 2008 09:42:23 -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/24/t12275450426twypfimdjkdv8z.htm/, Retrieved Mon, 24 Nov 2008 16:44:10 +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/24/t12275450426twypfimdjkdv8z.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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7,8 0 7,6 0 7,5 0 7,6 0 7,5 0 7,3 0 7,6 0 7,5 0 7,6 0 7,9 0 7,9 0 8,1 0 8,2 0 8,0 0 7,5 0 6,8 0 6,5 0 6,6 0 7,6 0 8,0 0 8,0 0 7,7 0 7,5 0 7,6 0 7,7 0 7,9 0 7,8 0 7,5 0 7,5 0 7,1 0 7,5 0 7,5 0 7,6 0 7,7 0 7,7 1 7,9 1 8,1 1 8,2 1 8,2 1 8,1 1 7,9 1 7,3 1 6,9 1 6,6 1 6,7 1 6,9 1 7,0 1 7,1 1 7,2 1 7,1 1 6,9 1 7,0 1 6,8 1 6,4 1 6,7 1 6,7 1 6,4 1 6,3 1 6,2 1 6,5 1 6,8 1 6,8 1 6,5 1 6,3 1 5,9 1 5,9 1 6,4 1 6,4 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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 7.57941176470589 -0.644117647058824x[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) 7.57941176470589 0.091319 82.9989 0 0 x -0.644117647058824 0.129145 -4.9875 5e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.523194814174468 R-squared 0.273732813579056 Adjusted R-squared 0.262728765299951 F-TEST (value) 24.8756463654224 F-TEST (DF numerator) 1 F-TEST (DF denominator) 66 p-value 4.7039272967897e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.532478983709866 Sum Squared Residuals 18.7132352941176 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 7.57941176470587 0.220588235294131 2 7.6 7.57941176470588 0.0205882352941174 3 7.5 7.57941176470588 -0.0794117647058827 4 7.6 7.57941176470588 0.0205882352941170 5 7.5 7.57941176470588 -0.0794117647058827 6 7.3 7.57941176470588 -0.279411764705883 7 7.6 7.57941176470588 0.0205882352941170 8 7.5 7.57941176470588 -0.0794117647058827 9 7.6 7.57941176470588 0.0205882352941170 10 7.9 7.57941176470588 0.320588235294118 11 7.9 7.57941176470588 0.320588235294118 12 8.1 7.57941176470588 0.520588235294117 13 8.2 7.57941176470588 0.620588235294117 14 8 7.57941176470588 0.420588235294117 15 7.5 7.57941176470588 -0.0794117647058827 16 6.8 7.57941176470588 -0.779411764705883 17 6.5 7.57941176470588 -1.07941176470588 18 6.6 7.57941176470588 -0.979411764705883 19 7.6 7.57941176470588 0.0205882352941170 20 8 7.57941176470588 0.420588235294117 21 8 7.57941176470588 0.420588235294117 22 7.7 7.57941176470588 0.120588235294117 23 7.5 7.57941176470588 -0.0794117647058827 24 7.6 7.57941176470588 0.0205882352941170 25 7.7 7.57941176470588 0.120588235294117 26 7.9 7.57941176470588 0.320588235294118 27 7.8 7.57941176470588 0.220588235294117 28 7.5 7.57941176470588 -0.0794117647058827 29 7.5 7.57941176470588 -0.0794117647058827 30 7.1 7.57941176470588 -0.479411764705883 31 7.5 7.57941176470588 -0.0794117647058827 32 7.5 7.57941176470588 -0.0794117647058827 33 7.6 7.57941176470588 0.0205882352941170 34 7.7 7.57941176470588 0.120588235294117 35 7.7 6.93529411764706 0.764705882352941 36 7.9 6.93529411764706 0.964705882352942 37 8.1 6.93529411764706 1.16470588235294 38 8.2 6.93529411764706 1.26470588235294 39 8.2 6.93529411764706 1.26470588235294 40 8.1 6.93529411764706 1.16470588235294 41 7.9 6.93529411764706 0.964705882352942 42 7.3 6.93529411764706 0.364705882352941 43 6.9 6.93529411764706 -0.0352941176470585 44 6.6 6.93529411764706 -0.335294117647059 45 6.7 6.93529411764706 -0.235294117647059 46 6.9 6.93529411764706 -0.0352941176470585 47 7 6.93529411764706 0.0647058823529412 48 7.1 6.93529411764706 0.164705882352941 49 7.2 6.93529411764706 0.264705882352941 50 7.1 6.93529411764706 0.164705882352941 51 6.9 6.93529411764706 -0.0352941176470585 52 7 6.93529411764706 0.0647058823529412 53 6.8 6.93529411764706 -0.135294117647059 54 6.4 6.93529411764706 -0.535294117647058 55 6.7 6.93529411764706 -0.235294117647059 56 6.7 6.93529411764706 -0.235294117647059 57 6.4 6.93529411764706 -0.535294117647058 58 6.3 6.93529411764706 -0.635294117647059 59 6.2 6.93529411764706 -0.735294117647059 60 6.5 6.93529411764706 -0.435294117647059 61 6.8 6.93529411764706 -0.135294117647059 62 6.8 6.93529411764706 -0.135294117647059 63 6.5 6.93529411764706 -0.435294117647059 64 6.3 6.93529411764706 -0.635294117647059 65 5.9 6.93529411764706 -1.03529411764706 66 5.9 6.93529411764706 -1.03529411764706 67 6.4 6.93529411764706 -0.535294117647058 68 6.4 6.93529411764706 -0.535294117647058

Charts produced by software:

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Parameters (Session):

par1 = 0 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 0 ; par2 = Do not include Seasonal 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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