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

Title produced by software: Multiple Regression

Date of computation: Sun, 25 Nov 2007 10:37:50 -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/25/t1196011715vin3dgr7ila1864.htm/, Retrieved Sun, 25 Nov 2007 18:28:45 +0100

User-defined keywords:

Dataseries X:

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8,7 0 8,5 0 8,2 0 8,3 0 8 0 8,1 0 8,7 0 9,3 0 8,9 0 8,8 0 8,4 0 8,4 0 7,3 0 7,2 0 7 0 7 0 6,9 0 6,9 0 7,1 0 7,5 0 7,4 0 8,9 0 8,3 1 8,3 1 9 1 8,9 1 8,8 1 7,8 1 7,8 1 7,8 1 9,2 1 9,3 1 9,2 1 8,6 1 8,5 1 8,5 1 9 1 9 1 8,8 1 8 1 7,9 1 8,1 1 9,3 1 9,4 1 9,4 1 9,3 1 9 1 9,1 1 9,7 1 9,7 1 9,6 1 8,3 1 8,2 1 8,4 1 10,6 1 10,9 1 10,9 1 9,6 1 9,3 1 9,3 1 9,6 1 9,5 1 9,5 1 9 1 8,9 1 9 1 10,1 1 10,2 1 10,2 1 9,5 1 9,3 1 9,3 1 9,4 1 9,3 1 9,1 1 9 1 8,9 1 9 1 9,8 1 10 1 9,8 1 9,4 1 9 1 8,9 1 9,3 1 9,1 1 8,8 1 8,9 1 8,7 1 8,6 1 9,1 1 9,3 1 8,9 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 WLHvrouwen[t] = + 7.88130050731213 + 0.7501586454157x[t] + 0.00834541043135596t + 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) 7.88130050731213 0.150624 52.3245 0 0 x 0.7501586454157 0.243415 3.0818 0.00273 0.001365 t 0.00834541043135596 0.003853 2.1658 0.032974 0.016487 Multiple Linear Regression - Regression Statistics Multiple R 0.60667350831097 R-squared 0.368052745686340 Adjusted R-squared 0.354009473368259 F-TEST (value) 26.2084745883947 F-TEST (DF numerator) 2 F-TEST (DF denominator) 90 p-value 1.07309316987880e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.675220809045129 Sum Squared Residuals 41.0330826870802 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 7.88964591774351 0.810354082256486 2 8.5 7.89799132817484 0.602008671825159 3 8.2 7.9063367386062 0.293663261393798 4 8.3 7.91468214903756 0.385317850962444 5 8 7.92302755946891 0.0769724405310875 6 8.1 7.93137296990027 0.168627030099731 7 8.7 7.93971838033162 0.760281619668375 8 9.3 7.94806379076298 1.35193620923702 9 8.9 7.95640920119434 0.943590798805664 10 8.8 7.9647546116257 0.835245388374308 11 8.4 7.97310002205705 0.426899977942952 12 8.4 7.9814454324884 0.418554567511596 13 7.3 7.98979084291976 -0.68979084291976 14 7.2 7.99813625335112 -0.798136253351116 15 7 8.00648166378247 -1.00648166378247 16 7 8.01482707421383 -1.01482707421383 17 6.9 8.02317248464518 -1.12317248464518 18 6.9 8.03151789507654 -1.13151789507654 19 7.1 8.0398633055079 -0.939863305507896 20 7.5 8.04820871593925 -0.548208715939252 21 7.4 8.05655412637061 -0.656554126370607 22 8.9 8.06489953680196 0.835100463198037 23 8.3 8.82340359264902 -0.52340359264902 24 8.3 8.83174900308038 -0.531749003080376 25 9 8.84009441351173 0.159905586488267 26 8.9 8.84843982394309 0.0515601760569119 27 8.8 8.85678523437444 -0.0567852343744437 28 7.8 8.8651306448058 -1.0651306448058 29 7.8 8.87347605523716 -1.07347605523716 30 7.8 8.88182146566851 -1.08182146566851 31 9.2 8.89016687609987 0.309833123900131 32 9.3 8.89851228653122 0.401487713468777 33 9.2 8.90685769696258 0.293142303037419 34 8.6 8.91520310739394 -0.315203107393937 35 8.5 8.9235485178253 -0.423548517825292 36 8.5 8.93189392825665 -0.431893928256648 37 9 8.940239338688 0.0597606613119961 38 9 8.94858474911936 0.0514152508806401 39 8.8 8.95693015955072 -0.156930159550715 40 8 8.96527556998207 -0.965275569982072 41 7.9 8.97362098041343 -1.07362098041343 42 8.1 8.98196639084478 -0.881966390844784 43 9.3 8.99031180127614 0.309688198723861 44 9.4 8.9986572117075 0.401342788292505 45 9.4 9.00700262213885 0.392997377861149 46 9.3 9.01534803257021 0.284651967429793 47 9 9.02369344300156 -0.0236934430015635 48 9.1 9.03203885343292 0.0679611465670802 49 9.7 9.04038426386428 0.659615736135724 50 9.7 9.04872967429563 0.651270325704368 51 9.6 9.05707508472699 0.542924915273012 52 8.3 9.06542049515834 -0.765420495158343 53 8.2 9.0737659055897 -0.8737659055897 54 8.4 9.08211131602106 -0.682111316021055 55 10.6 9.09045672645241 1.50954327354759 56 10.9 9.09880213688377 1.80119786311623 57 10.9 9.10714754731512 1.79285245268488 58 9.6 9.11549295774648 0.484507042253521 59 9.3 9.12383836817783 0.176161631822166 60 9.3 9.13218377860919 0.16781622139081 61 9.6 9.14052918904055 0.459470810959453 62 9.5 9.1488745994719 0.351125400528097 63 9.5 9.15722000990326 0.342779990096741 64 9 9.16556542033461 -0.165565420334615 65 8.9 9.17391083076597 -0.27391083076597 66 9 9.18225624119733 -0.182256241197327 67 10.1 9.19060165162868 0.909398348371317 68 10.2 9.19894706206004 1.00105293793996 69 10.2 9.2072924724914 0.992707527508605 70 9.5 9.21563788292275 0.284362117077250 71 9.3 9.2239832933541 0.0760167066458944 72 9.3 9.23232870378546 0.0676712962145384 73 9.4 9.24067411421682 0.159325885783182 74 9.3 9.24901952464817 0.0509804753518265 75 9.1 9.25736493507953 -0.157364935079531 76 9 9.26571034551089 -0.265710345510886 77 8.9 9.27405575594224 -0.374055755942242 78 9 9.2824011663736 -0.282401166373598 79 9.8 9.29074657680495 0.509253423195047 80 10 9.2990919872363 0.70090801276369 81 9.8 9.30743739766767 0.492562602332335 82 9.4 9.31578280809902 0.0842171919009785 83 9 9.32412821853038 -0.324128218530378 84 8.9 9.33247362896173 -0.432473628961733 85 9.3 9.34081903939309 -0.040819039393089 86 9.1 9.34916444982445 -0.249164449824446 87 8.8 9.3575098602558 -0.557509860255801 88 8.9 9.36585527068716 -0.465855270687157 89 8.7 9.37420068111851 -0.674200681118514 90 8.6 9.38254609154987 -0.78254609154987 91 9.1 9.39089150198123 -0.290891501981226 92 9.3 9.39923691241258 -0.0992369124125806 93 8.9 9.40758232284394 -0.507582322843937

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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