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Workshop: Seatbelt Law _ Eigen geg.

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 13:05:00 -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/22/t11957615098fygnarq5hxprhm.htm/, Retrieved Thu, 22 Nov 2007 20:58:29 +0100

User-defined keywords:

Tinne Van der Eycken Workshop 2 zonder seizoenaliteit

Dataseries X:

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0.9811 0 1.0014 0 1.0183 0 1.0622 0 1.0773 0 1.0807 0 1.0848 0 1.1582 0 1.1663 0 1.1372 0 1.1139 0 1.1222 0 1.1692 0 1.1702 0 1.2286 0 1.2613 0 1.2646 0 1.2262 0 1.1985 0 1.2007 0 1.2138 0 1.2266 0 1.2176 0 1.2218 0 1.249 0 1.2991 0 1.3408 0 1.3119 0 1.3014 0 1.3201 0 1.2938 0 1.2694 0 1.2165 0 1.2037 0 1.2292 0 1.2256 0 1.2015 0 1.1786 0 1.1856 0 1.2103 0 1.1938 0 1.202 0 1.2271 0 1.277 0 1.265 0 1.2684 0 1.2811 0 1.2727 0 1.2611 0 1.2881 1 1.3213 1 1.2999 1 1.3074 1 1.3242 1 1.3516 1 1.3511 1 1.3419 1 1.3716 1 1.3622 1 1.3896 1 1.4227 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.09847380723183 + 0.0164782897207963X[t] + 0.00413239464950216t + 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) 1.09847380723183 0.016016 68.5855 0 0 X 0.0164782897207963 0.024654 0.6684 0.506539 0.25327 t 0.00413239464950216 0.000557 7.424 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.81957385440527 R-squared 0.671701302824711 Adjusted R-squared 0.660380658094529 F-TEST (value) 59.3341915442205 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 9.32587340685131e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0555037188288364 Sum Squared Residuals 0.178678442622171 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.9811 1.10260620188133 -0.121506201881335 2 1.0014 1.10673859653084 -0.105338596530838 3 1.0183 1.11087099118034 -0.0925709911803402 4 1.0622 1.11500338582984 -0.0528033858298423 5 1.0773 1.11913578047934 -0.0418357804793446 6 1.0807 1.12326817512885 -0.0425681751288467 7 1.0848 1.12740056977835 -0.0426005697783489 8 1.1582 1.13153296442785 0.0266670355721489 9 1.1663 1.13566535907735 0.0306346409226467 10 1.1372 1.13979775372686 -0.00259775372685536 11 1.1139 1.14393014837636 -0.0300301483763576 12 1.1222 1.14806254302586 -0.0258625430258596 13 1.1692 1.15219493767536 0.0170050623246382 14 1.1702 1.15632733232486 0.0138726676751359 15 1.2286 1.16045972697437 0.0681402730256338 16 1.2613 1.16459212162387 0.0967078783761318 17 1.2646 1.16872451627337 0.0958754837266295 18 1.2262 1.17285691092287 0.0533430890771273 19 1.1985 1.17698930557237 0.0215106944276251 20 1.2007 1.18112170022188 0.0195782997781231 21 1.2138 1.18525409487138 0.0285459051286209 22 1.2266 1.18938648952088 0.0372135104791186 23 1.2176 1.19351888417038 0.0240811158296166 24 1.2218 1.19765127881989 0.0241487211801144 25 1.249 1.20178367346939 0.0472163265306123 26 1.2991 1.20591606811889 0.09318393188111 27 1.3408 1.21004846276839 0.130751537231608 28 1.3119 1.21418085741789 0.0977191425821058 29 1.3014 1.21831325206740 0.0830867479326035 30 1.3201 1.22244564671690 0.0976543532831015 31 1.2938 1.2265780413664 0.0672219586335993 32 1.2694 1.23071043601590 0.0386895639840972 33 1.2165 1.23484283066541 -0.0183428306654051 34 1.2037 1.23897522531491 -0.0352752253149072 35 1.2292 1.24310761996441 -0.0139076199644093 36 1.2256 1.24724001461391 -0.0216400146139115 37 1.2015 1.25137240926341 -0.0498724092634137 38 1.1786 1.25550480391292 -0.0769048039129158 39 1.1856 1.25963719856242 -0.074037198562418 40 1.2103 1.26376959321192 -0.0534695932119202 41 1.1938 1.26790198786142 -0.0741019878614224 42 1.202 1.27203438251092 -0.0700343825109245 43 1.2271 1.27616677716043 -0.0490667771604266 44 1.277 1.28029917180993 -0.00329917180992891 45 1.265 1.28443156645943 -0.0194315664594311 46 1.2684 1.28856396110893 -0.0201639611089332 47 1.2811 1.29269635575844 -0.0115963557584354 48 1.2727 1.29682875040794 -0.0241287504079375 49 1.2611 1.30096114505744 -0.0398611450574395 50 1.2881 1.32157182942774 -0.0334718294277381 51 1.3213 1.32570422407724 -0.00440422407724035 52 1.2999 1.32983661872674 -0.0299366187267424 53 1.3074 1.33396901337624 -0.0265690133762447 54 1.3242 1.33810140802575 -0.0139014080257467 55 1.3516 1.34223380267525 0.009366197324751 56 1.3511 1.34636619732475 0.0047338026752489 57 1.3419 1.35049859197425 -0.00859859197425313 58 1.3716 1.35463098662376 0.0169690133762445 59 1.3622 1.35876338127326 0.00343661872674253 60 1.3896 1.36289577592276 0.0267042240772403 61 1.4227 1.36702817057226 0.0556718294277382

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal 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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