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Case: 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: Sat, 17 Nov 2007 05:51:42 -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/17/t1195303787kmxb856ne4hqta7.htm/, Retrieved Sat, 17 Nov 2007 13:49:57 +0100

User-defined keywords:

Dataseries X:

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105,3 0 103 0 103,8 0 103,4 0 105,8 0 101,4 0 97 0 94,3 0 96,6 0 97,1 0 95,7 0 96,9 0 97,4 0 95,3 0 93,6 0 91,5 0 93,1 0 91,7 0 94,3 0 93,9 0 90,9 0 88,3 0 91,3 0 91,7 0 92,4 1 92 1 95,6 1 95,8 1 96,4 1 99 1 107 1 109,7 1 116,2 1 115,9 1 113,8 1 112,6 1 113,7 1 115,9 1 110,3 1 111,3 1 113,4 1 108,2 1 104,8 1 106 1 110,9 1 115 1 118,4 1 121,4 1 128,8 1 131,7 1 141,7 1 142,9 1 139,4 1 134,7 1 125 1 113,6 1 111,5 1 108,5 1 112,3 1 116,6 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 y[t] = + 86.4666666666666 -0.486111111111113x[t] + 6.29986111111108M1[t] + 5.75805555555558M2[t] + 6.57625M3[t] + 5.95444444444444M4[t] + 5.99263888888889M5[t] + 2.77083333333334M6[t] + 0.789027777777779M7[t] -1.93277777777778M8[t] -0.81458333333333M9[t] -1.67638888888889M10[t] -0.938194444444444M11[t] + 0.601805555555556t + 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) 86.4666666666666 5.544557 15.5949 0 0 x -0.486111111111113 5.335253 -0.0911 0.927798 0.463899 M1 6.29986111111108 6.622666 0.9513 0.346445 0.173223 M2 5.75805555555558 6.58495 0.8744 0.386429 0.193214 M3 6.57625 6.550639 1.0039 0.320674 0.160337 M4 5.95444444444444 6.519787 0.9133 0.365853 0.182927 M5 5.99263888888889 6.492442 0.923 0.360814 0.180407 M6 2.77083333333334 6.46865 0.4283 0.670397 0.335198 M7 0.789027777777779 6.44845 0.1224 0.903147 0.451574 M8 -1.93277777777778 6.431875 -0.3005 0.76515 0.382575 M9 -0.81458333333333 6.418954 -0.1269 0.89957 0.449785 M10 -1.67638888888889 6.409709 -0.2615 0.794844 0.397422 M11 -0.938194444444444 6.404156 -0.1465 0.884169 0.442084 t 0.601805555555556 0.154015 3.9074 0.000304 0.000152 Multiple Linear Regression - Regression Statistics Multiple R 0.753689999567463 R-squared 0.568048615448002 Adjusted R-squared 0.445975398074612 F-TEST (value) 4.65334352342404 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.84532670212978e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.1229305155287 Sum Squared Residuals 4713.79122222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.3 93.3683333333335 11.9316666666665 2 103 93.4283333333333 9.57166666666668 3 103.8 94.8483333333333 8.95166666666667 4 103.4 94.8283333333333 8.57166666666667 5 105.8 95.4683333333333 10.3316666666667 6 101.4 92.8483333333333 8.55166666666667 7 97 91.4683333333333 5.53166666666668 8 94.3 89.3483333333333 4.95166666666667 9 96.6 91.0683333333333 5.53166666666666 10 97.1 90.8083333333333 6.29166666666667 11 95.7 92.1483333333333 3.55166666666667 12 96.9 93.6883333333333 3.21166666666668 13 97.4 100.59 -3.18999999999996 14 95.3 100.65 -5.35000000000001 15 93.6 102.07 -8.47 16 91.5 102.05 -10.55 17 93.1 102.69 -9.59 18 91.7 100.07 -8.37 19 94.3 98.69 -4.39 20 93.9 96.57 -2.66999999999999 21 90.9 98.29 -7.39 22 88.3 98.03 -9.73 23 91.3 99.37 -8.07 24 91.7 100.91 -9.21 25 92.4 107.325555555556 -14.9255555555555 26 92 107.385555555556 -15.3855555555556 27 95.6 108.805555555556 -13.2055555555556 28 95.8 108.785555555556 -12.9855555555556 29 96.4 109.425555555556 -13.0255555555555 30 99 106.805555555556 -7.80555555555555 31 107 105.425555555556 1.57444444444444 32 109.7 103.305555555556 6.39444444444444 33 116.2 105.025555555556 11.1744444444444 34 115.9 104.765555555556 11.1344444444444 35 113.8 106.105555555556 7.69444444444444 36 112.6 107.645555555556 4.95444444444444 37 113.7 114.547222222222 -0.847222222222193 38 115.9 114.607222222222 1.29277777777777 39 110.3 116.027222222222 -5.72722222222222 40 111.3 116.007222222222 -4.70722222222223 41 113.4 116.647222222222 -3.24722222222222 42 108.2 114.027222222222 -5.82722222222222 43 104.8 112.647222222222 -7.84722222222223 44 106 110.527222222222 -4.52722222222223 45 110.9 112.247222222222 -1.34722222222222 46 115 111.987222222222 3.01277777777777 47 118.4 113.327222222222 5.07277777777778 48 121.4 114.867222222222 6.53277777777778 49 128.8 121.768888888889 7.03111111111115 50 131.7 121.828888888889 9.8711111111111 51 141.7 123.248888888889 18.4511111111111 52 142.9 123.228888888889 19.6711111111111 53 139.4 123.868888888889 15.5311111111111 54 134.7 121.248888888889 13.4511111111111 55 125 119.868888888889 5.13111111111111 56 113.6 117.748888888889 -4.1488888888889 57 111.5 119.468888888889 -7.9688888888889 58 108.5 119.208888888889 -10.7088888888889 59 112.3 120.548888888889 -8.2488888888889 60 116.6 122.088888888889 -5.4888888888889

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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