Seatbelt Law Q3 eigen tijdreeks

*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: Sun, 23 Nov 2008 15:57:41 -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/t1227481175j5krlvxiurw7x0d.htm/, Retrieved Sun, 23 Nov 2008 22:59:35 +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/t1227481175j5krlvxiurw7x0d.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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Dataseries X:

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24,67 0 25,59 0 26,09 0 28,37 0 27,34 0 24,46 0 27,46 0 30,23 0 32,33 0 29,87 0 24,87 0 25,48 0 27,28 0 28,24 0 29,58 0 26,95 0 29,08 0 28,76 0 29,59 0 30,7 0 30,52 0 32,67 0 33,19 0 37,13 0 35,54 0 37,75 0 41,84 0 42,94 0 49,14 0 44,61 0 40,22 0 44,23 0 45,85 0 53,38 0 53,26 0 51,8 0 55,3 0 57,81 0 63,96 0 63,77 0 59,15 0 56,12 0 57,42 0 63,52 0 61,71 0 63,01 0 68,18 0 72,03 0 69,75 0 74,41 0 74,33 0 64,24 1 60,03 1 59,44 1 62,5 1 55,04 1 58,34 1 61,92 0 67,65 0 67,68 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 16.0411666666667 -9.65694444444445D[t] + 2.31208796296296M1[t] + 3.59789814814815M2[t] + 5.03170833333333M3[t] + 4.09090740740741M4[t] + 2.81871759259260M5[t] -0.417472222222220M6[t] -0.623662037037035M7[t] -0.283851851851850M8[t] -0.244041666666662M9[t] -0.721620370370367M10[t] -0.427810185185180M11[t] + 0.966189814814815t + 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) 16.0411666666667 2.946586 5.444 2e-06 1e-06 D -9.65694444444445 2.835354 -3.4059 0.001378 0.000689 M1 2.31208796296296 3.441904 0.6717 0.505105 0.252552 M2 3.59789814814815 3.435085 1.0474 0.300389 0.150194 M3 5.03170833333333 3.428903 1.4674 0.149061 0.074531 M4 4.09090740740741 3.500766 1.1686 0.248596 0.124298 M5 2.81871759259260 3.492144 0.8072 0.423729 0.211864 M6 -0.417472222222220 3.484141 -0.1198 0.905147 0.452573 M7 -0.623662037037035 3.476763 -0.1794 0.858427 0.429214 M8 -0.283851851851850 3.470012 -0.0818 0.93516 0.46758 M9 -0.244041666666662 3.463893 -0.0705 0.944139 0.472069 M10 -0.721620370370367 3.403737 -0.212 0.833037 0.416519 M11 -0.427810185185180 3.402753 -0.1257 0.900498 0.450249 t 0.966189814814815 0.047256 20.4459 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.95637706316928 R-squared 0.914657086956299 Adjusted R-squared 0.890538437617861 F-TEST (value) 37.923230033393 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.37970616127336 Sum Squared Residuals 1331.29696555556 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24.67 19.3194444444444 5.35055555555555 2 25.59 21.5714444444444 4.01855555555556 3 26.09 23.9714444444444 2.11855555555556 4 28.37 23.9968333333333 4.37316666666666 5 27.34 23.6908333333333 3.64916666666668 6 24.46 21.4208333333333 3.03916666666666 7 27.46 22.1808333333333 5.27916666666667 8 30.23 23.4868333333333 6.74316666666667 9 32.33 24.4928333333333 7.83716666666666 10 29.87 24.9814444444444 4.88855555555556 11 24.87 26.2414444444444 -1.37144444444445 12 25.48 27.6354444444444 -2.15544444444445 13 27.28 30.9137222222222 -3.63372222222221 14 28.24 33.1657222222222 -4.92572222222224 15 29.58 35.5657222222222 -5.98572222222222 16 26.95 35.5911111111111 -8.6411111111111 17 29.08 35.2851111111111 -6.20511111111111 18 28.76 33.0151111111111 -4.25511111111111 19 29.59 33.7751111111111 -4.18511111111111 20 30.7 35.0811111111111 -4.38111111111111 21 30.52 36.0871111111111 -5.56711111111111 22 32.67 36.5757222222222 -3.90572222222222 23 33.19 37.8357222222222 -4.64572222222223 24 37.13 39.2297222222222 -2.09972222222222 25 35.54 42.508 -6.968 26 37.75 44.76 -7.00999999999999 27 41.84 47.16 -5.32 28 42.94 47.1853888888889 -4.24538888888889 29 49.14 46.8793888888889 2.26061111111111 30 44.61 44.6093888888889 0.000611111111112331 31 40.22 45.3693888888889 -5.14938888888889 32 44.23 46.6753888888889 -2.44538888888890 33 45.85 47.6813888888889 -1.83138888888889 34 53.38 48.17 5.21 35 53.26 49.43 3.82999999999999 36 51.8 50.824 0.975999999999995 37 55.3 54.1022777777778 1.19772222222221 38 57.81 56.3542777777778 1.45572222222223 39 63.96 58.7542777777778 5.20572222222222 40 63.77 58.7796666666667 4.99033333333334 41 59.15 58.4736666666667 0.676333333333324 42 56.12 56.2036666666667 -0.0836666666666691 43 57.42 56.9636666666667 0.456333333333329 44 63.52 58.2696666666667 5.25033333333334 45 61.71 59.2756666666667 2.43433333333333 46 63.01 59.7642777777778 3.24572222222222 47 68.18 61.0242777777778 7.15572222222223 48 72.03 62.4182777777778 9.61172222222221 49 69.75 65.6965555555555 4.05344444444445 50 74.41 67.9485555555556 6.46144444444444 51 74.33 70.3485555555556 3.98144444444444 52 64.24 60.717 3.52300000000000 53 60.03 60.411 -0.380999999999998 54 59.44 58.141 1.299 55 62.5 58.901 3.599 56 55.04 60.207 -5.167 57 58.34 61.213 -2.873 58 61.92 71.3585555555556 -9.43855555555556 59 67.65 72.6185555555555 -4.96855555555555 60 67.68 74.0125555555556 -6.33255555555554

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) 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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