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The Seatbelt Law Q3

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 09:53:00 -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/18/t1195404393byqbop09kdhyv8b.htm/, Retrieved Sun, 18 Nov 2007 17:46:43 +0100

User-defined keywords:

The Seatbelt Law Q3

Dataseries X:

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117 126,6 103,8 93,9 100,8 89,8 110,6 93,4 104 101,5 112,6 110,4 107,3 105,9 98,9 108,4 109,8 113,9 104,9 86,1 102,2 69,4 123,9 101,2 124,9 100,5 112,7 98 121,9 106,6 100,6 90,1 104,3 96,9 120,4 125,9 107,5 112 102,9 100 125,6 123,9 107,5 79,8 108,8 83,4 128,4 113,6 121,1 112,9 119,5 104 128,7 109,9 108,7 99 105,5 106,3 119,8 128,9 111,3 111,1 110,6 102,9 120,1 130 97,5 87 107,7 87,5 127,3 117,6 117,2 103,4 119,8 110,8 116,2 112,6 111 102,5 112,4 112,4 130,6 135,6 109,1 105,1 118,8 127,7 123,9 137 101,6 91 112,8 90,5 128 122,4 129,6 123,3 125,8 124,3 119,5 120 115,7 118,1 113,6 119 129,7 142,7 112 123,6 116,8 129,6 127 151,6 112,9 108,7 113,3 99,3 121,7 126,4

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 Consumptiegoederen[t] = + 89.0024026280987 + 0.291830859689179`Investeringsgoederen `[t] -2.15683048862524M1[t] -5.79469087937866M2[t] -5.23731636662177M3[t] -11.3293401401814M4[t] -14.6969565430642M5[t] -6.387016138122M6[t] -14.6407313147899M7[t] -15.1984553178465M8[t] -8.72453794292267M9[t] -13.3110448309259M10[t] -7.9993386912588M11[t] + 0.081532728934197t + 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) 89.0024026280987 10.246328 8.6863 0 0 `Investeringsgoederen ` 0.291830859689179 0.100617 2.9004 0.005698 0.002849 M1 -2.15683048862524 2.96715 -0.7269 0.470969 0.235484 M2 -5.79469087937866 2.999509 -1.9319 0.059548 0.029774 M3 -5.23731636662177 2.978128 -1.7586 0.085298 0.042649 M4 -11.3293401401814 3.174651 -3.5687 0.000852 0.000426 M5 -14.6969565430642 2.9967 -4.9044 1.2e-05 6e-06 M6 -6.387016138122 3.320303 -1.9236 0.060603 0.030301 M7 -14.6407313147899 2.946203 -4.9694 1e-05 5e-06 M8 -15.1984553178465 2.935844 -5.1769 5e-06 2e-06 M9 -8.72453794292267 3.370058 -2.5888 0.012849 0.006425 M10 -13.3110448309259 3.847882 -3.4593 0.001178 0.000589 M11 -7.9993386912588 4.189334 -1.9095 0.062452 0.031226 t 0.081532728934197 0.059874 1.3617 0.179912 0.089956 Multiple Linear Regression - Regression Statistics Multiple R 0.890455765467203 R-squared 0.792911470253783 Adjusted R-squared 0.734386450977678 F-TEST (value) 13.5482479127951 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.21763710225764e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.63564459606906 Sum Squared Residuals 988.503237768956 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 117 123.872891705058 -6.87289170505791 2 103.8 110.773694931402 -6.97369493140236 3 100.8 110.216095648368 -9.41609564836783 4 110.6 105.256195698623 5.34380430137659 5 104 104.333941988157 -0.333941988157167 6 112.6 115.322709773267 -2.72270977326730 7 107.3 105.837288456932 1.4627115430677 8 98.9 106.090674332033 -7.19067433203283 9 109.8 114.251194164181 -4.45119416418134 10 104.9 101.633322105753 3.2666778942469 11 102.2 102.152985617545 0.0470143824548923 12 123.9 119.514078375854 4.38592162414599 13 124.9 117.234499014381 7.66550098561947 14 112.7 112.948594203338 -0.248594203338367 15 121.9 116.097246838356 5.8027531616436 16 100.6 105.271546608859 -4.67154660885947 17 104.3 103.969912780797 0.330087219202691 18 120.4 120.82448084566 -0.424480845659924 19 107.5 108.595849448247 -1.09584944824666 20 102.9 104.617687857854 -1.71768785785409 21 125.6 118.147895508283 7.4521044917165 22 107.5 100.773180436922 6.72681956307837 23 108.8 107.217010400404 1.58298959959601 24 128.4 124.111173783210 4.28882621678981 25 121.1 121.831594421737 -0.73159442173674 26 119.5 115.677972108684 3.82202789131619 27 128.7 118.038681422541 10.6613185774589 28 108.7 108.847234007304 -0.147234007303526 29 105.5 107.691515609086 -2.19151560908595 30 119.8 122.678366171938 -2.87836617193784 31 111.3 109.311594421737 1.98840557826324 32 110.6 106.442390098163 4.15760990183691 33 120.1 120.906456499598 -0.806456499597854 34 97.5 103.852755373894 -6.35275537389409 35 107.7 109.39190967234 -1.69190967233998 36 127.3 126.256889969177 1.04311003082272 37 117.2 120.03759400190 -2.83759400189989 38 119.8 118.640814701781 1.15918529821941 39 116.2 119.805017490912 -3.6050174909122 40 111 110.847034763426 0.152965236573982 41 112.4 110.450076600400 1.94992339959969 42 130.6 125.612025679066 4.9879743209343 43 109.1 108.539002010812 0.560997989187948 44 118.8 114.658188165665 4.14181183433490 45 123.9 123.927665264632 -0.0276652646324652 46 101.6 105.998471559861 -4.39847155986117 47 112.8 111.245794998618 1.55420500138211 48 128 128.636070842896 -0.636070842895708 49 129.6 126.823420856925 2.77657914307507 50 125.8 123.558924054795 2.24107594520512 51 119.5 122.942958599822 -3.44295859982250 52 115.7 116.377988921788 -0.677988921787573 53 113.6 113.354553021559 0.245446978440737 54 129.7 128.662417530069 1.03758246993076 55 112 114.916265662272 -2.91626566227223 56 116.8 116.191059546285 0.608940453715108 57 127 129.166788563305 -2.16678856330484 58 112.9 112.14227052357 0.757729476429997 59 113.3 114.792299311093 -1.49229931109303 60 121.7 130.781787028863 -9.08178702886279

Charts produced by software:

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Parameters:

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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Software written by Ed van Stee & Patrick Wessa

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