Seatbelt law - Q3 Multiple Regression

*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: Wed, 19 Nov 2008 11:53:10 -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/19/t1227120949c5rljtocc8d3fcp.htm/, Retrieved Wed, 19 Nov 2008 18:55:49 +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/19/t1227120949c5rljtocc8d3fcp.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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10.413 0 10.709 0 10.662 0 10.570 0 10.297 0 10.635 0 10.872 0 10.296 0 10.383 0 10.431 0 10.574 0 10.653 0 10.805 0 10.872 0 10.625 0 10.407 0 10.463 0 10.556 0 10.646 0 10.702 0 11.353 1 11.346 1 11.451 1 11.964 1 12.574 1 13.031 1 13.812 1 14.544 1 14.931 1 14.886 1 16.005 1 17.064 1 15.168 1 16.050 1 15.839 1 15.137 1 14.954 1 15.648 1 15.305 1 15.579 1 16.348 1 15.928 1 16.171 1 15.937 1 15.713 1 15.594 1 15.683 1 16.438 1 17.032 1 17.696 1 17.745 1 19.394 1 20.148 1 20.108 1 18.584 1 18.441 1 18.391 1 19.178 1 18.079 1 18.483 1 19.644 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Goudkoers[t] = + 8.2133625 + 0.772593750000001DrasticChange[t] + 0.597173958333333M1[t] + 0.795041666666667M2[t] + 0.675209375M3[t] + 0.985777083333333M4[t] + 1.16594479166667M5[t] + 0.9927125M6[t] + 0.867280208333333M7[t] + 0.741247916666666M8[t] + 0.141896874999999M9[t] + 0.301664583333333M10[t] -0.0513677083333329M11[t] + 0.158432291666667t + 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) 8.2133625 0.532591 15.4215 0 0 DrasticChange 0.772593750000001 0.488427 1.5818 0.120402 0.060201 M1 0.597173958333333 0.621106 0.9615 0.341238 0.170619 M2 0.795041666666667 0.651831 1.2197 0.228662 0.114331 M3 0.675209375 0.65096 1.0373 0.304926 0.152463 M4 0.985777083333333 0.650346 1.5158 0.136274 0.068137 M5 1.16594479166667 0.64999 1.7938 0.079282 0.039641 M6 0.9927125 0.649893 1.5275 0.133339 0.066669 M7 0.867280208333333 0.650054 1.3342 0.188578 0.094289 M8 0.741247916666666 0.650474 1.1396 0.260248 0.130124 M9 0.141896874999999 0.64856 0.2188 0.827763 0.413881 M10 0.301664583333333 0.647912 0.4656 0.643656 0.321828 M11 -0.0513677083333329 0.647523 -0.0793 0.937107 0.468554 t 0.158432291666667 0.012963 12.2215 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.959503406781168 R-squared 0.920646787624667 Adjusted R-squared 0.898698026754894 F-TEST (value) 41.945273953599 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.02361855058467 Sum Squared Residuals 49.24636204375 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10.413 8.96896875 1.44403125 2 10.709 9.32526875 1.38373125 3 10.662 9.36386875 1.29813125 4 10.57 9.83286875 0.73713125 5 10.297 10.17146875 0.125531250000001 6 10.635 10.15666875 0.47833125 7 10.872 10.18966875 0.68233125 8 10.296 10.22206875 0.0739312499999999 9 10.383 9.78115 0.60185 10 10.431 10.09935 0.331649999999998 11 10.574 9.90475 0.66925 12 10.653 10.11455 0.53845 13 10.805 10.87015625 -0.0651562500000002 14 10.872 11.22645625 -0.354456250000001 15 10.625 11.26505625 -0.64005625 16 10.407 11.73405625 -1.32705625 17 10.463 12.07265625 -1.60965625 18 10.556 12.05785625 -1.50185625 19 10.646 12.09085625 -1.44485625 20 10.702 12.12325625 -1.42125625 21 11.353 12.45493125 -1.10193125000000 22 11.346 12.77313125 -1.42713125 23 11.451 12.57853125 -1.12753125000000 24 11.964 12.78833125 -0.82433125 25 12.574 13.5439375 -0.9699375 26 13.031 13.9002375 -0.8692375 27 13.812 13.9388375 -0.126837500000000 28 14.544 14.4078375 0.136162500000000 29 14.931 14.7464375 0.184562499999999 30 14.886 14.7316375 0.154362499999999 31 16.005 14.7646375 1.2403625 32 17.064 14.7970375 2.2669625 33 15.168 14.35611875 0.81188125 34 16.05 14.67431875 1.37568125 35 15.839 14.47971875 1.35928125 36 15.137 14.68951875 0.44748125 37 14.954 15.445125 -0.491125 38 15.648 15.801425 -0.153425000000001 39 15.305 15.840025 -0.535025 40 15.579 16.309025 -0.730025 41 16.348 16.647625 -0.299625000000001 42 15.928 16.632825 -0.704825 43 16.171 16.665825 -0.494825000000001 44 15.937 16.698225 -0.761225 45 15.713 16.25730625 -0.54430625 46 15.594 16.57550625 -0.981506250000001 47 15.683 16.38090625 -0.697906250000001 48 16.438 16.59070625 -0.152706250000001 49 17.032 17.3463125 -0.314312500000000 50 17.696 17.7026125 -0.00661249999999896 51 17.745 17.7412125 0.00378750000000093 52 19.394 18.2102125 1.18378750000000 53 20.148 18.5488125 1.5991875 54 20.108 18.5340125 1.57398750000000 55 18.584 18.5670125 0.0169875000000003 56 18.441 18.5994125 -0.158412500000000 57 18.391 18.15849375 0.232506249999999 58 19.178 18.47669375 0.70130625 59 18.079 18.28209375 -0.203093750000000 60 18.483 18.49189375 -0.0088937499999988 61 19.644 19.2475 0.396499999999999

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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Software written by Ed van Stee & Patrick Wessa

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