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Multiple lineair regression

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

Title produced by software: Multiple Regression

Date of computation: Sat, 22 Dec 2007 09:30:31 -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/Dec/22/t1198339934ugo23igddcoytxn.htm/, Retrieved Sat, 22 Dec 2007 17:12:29 +0100

User-defined keywords:

Goudkoers Inflatie

Dataseries X:

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10511 1.1 10812 1.3 10738 1.2 10171 1.6 9721 1.7 9897 1.5 9828 0.9 9924 1.5 10371 1.4 10846 1.6 10413 1.7 10709 1.4 10662 1.8 10570 1.7 10297 1.4 10635 1.2 10872 1 10296 1.7 10383 2.4 10431 2 10574 2.1 10653 2 10805 1.8 10872 2.7 10625 2.3 10407 1.9 10463 2 10556 2.3 10646 2.8 10702 2.4 11353 2.3 11346 2.7 11451 2.7 11964 2.9 12574 3 13031 2.2 13812 2.3 14544 2.8 14931 2.8 14886 2.8 16005 2.2 17064 2.6 15168 2.8 16050 2.5 15839 2.4 15137 2.3 14954 1.9 15648 1.7 15305 2 15579 2.1 16348 1.7 15928 1.8 16171 1.8 15937 1.8 15713 1.3 15594 1.3 15683 1.3 16438 1.2 17032 1.4 17696 2.2

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 Goud[t] = + 9521.03968922578 -485.323390468976inflatie[t] + 70.033067018788M1[t] + 157.990803021074M2[t] + 122.483860929558M3[t] -80.0389996400236M4[t] + 7.78639731535772M5[t] + 11.9570689363958M6[t] -447.924001917602M7[t] -379.366265915322M8[t] -415.034401150561M9[t] -321.889600767041M10[t] -333.86420381166M11[t] + 140.561667425859t + 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) 9521.03968922578 778.055675 12.237 0 0 inflatie -485.323390468976 286.152717 -1.696 0.096639 0.04832 M1 70.033067018788 736.711412 0.0951 0.924679 0.462339 M2 157.990803021074 735.537373 0.2148 0.830875 0.415438 M3 122.483860929558 735.575189 0.1665 0.868482 0.434241 M4 -80.0389996400236 733.676362 -0.1091 0.913603 0.456802 M5 7.78639731535772 733.166242 0.0106 0.991572 0.495786 M6 11.9570689363958 732.1778 0.0163 0.987041 0.493521 M7 -447.924001917602 731.746783 -0.6121 0.543466 0.271733 M8 -379.366265915322 731.110496 -0.5189 0.606325 0.303162 M9 -415.034401150561 730.798946 -0.5679 0.572852 0.286426 M10 -321.889600767041 730.502495 -0.4406 0.661537 0.330768 M11 -333.86420381166 730.59874 -0.457 0.649841 0.32492 t 140.561667425859 9.172729 15.3239 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.91870547257001 R-squared 0.844019745330085 Adjusted R-squared 0.799938369010327 F-TEST (value) 19.1468555611266 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.48689957516035e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1154.65073860238 Sum Squared Residuals 61328043.095131 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10511 9197.77869415459 1313.22130584542 2 10812 9329.2334194889 1482.7665805111 3 10738 9482.82048387014 1255.17951612986 4 10171 9226.72993453882 944.270065461176 5 9721 9406.58465987317 314.415340126828 6 9897 9648.38167701386 248.618322986138 7 9828 9620.2563078671 207.743692132889 8 9924 9538.18167701386 385.818322986137 9 10371 9691.60754825138 679.392451748619 10 10846 9828.24933796697 1017.75066203303 11 10413 9908.30406330131 504.695936698691 12 10709 10528.3269516795 180.673048320477 13 10662 10544.7923299366 117.207670063421 14 10570 10821.8440724116 -251.844072411618 15 10297 11072.4958148867 -775.495814886657 16 10635 11107.5992998367 -472.599299836731 17 10872 11433.0510423118 -561.051042311765 18 10296 11238.0570080304 -942.057008030382 19 10383 10579.0112312740 -196.011231273959 20 10431 10982.2599908897 -551.259990889688 21 10574 11038.6211840334 -464.621184033411 22 10653 11320.8599908897 -667.859990889688 23 10805 11546.5117333647 -741.511733364724 24 10872 11584.1465531802 -712.146553180164 25 10625 11988.8706438124 -1363.87064381240 26 10407 12411.5194034281 -2004.51940342814 27 10463 12468.0417897156 -2005.04178971558 28 10556 12260.4835794312 -1704.48357943117 29 10646 12246.2089485779 -1600.20894857792 30 10702 12585.0706438124 -1883.07064381241 31 11353 12314.2835794312 -961.283579431169 32 11346 12329.2736266717 -983.273626671717 33 11451 12434.1671588623 -983.167158862338 34 11964 12570.8089485779 -606.808948577922 35 12574 12650.8636739123 -76.8636739122658 36 13031 13513.5482575250 -482.548257524965 37 13812 13675.6106529227 136.389347077286 38 14544 13661.4683611164 882.531638883626 39 14931 13766.5230864507 1164.47691354928 40 14886 13704.561893307 1181.43810669301 41 16005 14224.1429919696 1780.85700803038 42 17064 14174.7459748289 2889.25402517107 43 15168 13758.361893307 1409.63810669301 44 16050 14113.0783138758 1936.92168612418 45 15839 14266.5041851133 1572.49581488666 46 15137 14548.7429919696 588.257008030381 47 14954 14871.4594125385 82.5405874615483 48 15648 15442.9499618698 205.050038130236 49 15305 15507.9476791737 -202.947679173718 50 15579 15687.9347435550 -108.934743554969 51 16348 15987.1188250769 360.881174923100 52 15928 15876.6252928863 51.3747071137194 53 16171 16105.0123572675 65.9876427324785 54 15937 16249.7446963144 -312.744696314419 55 15713 16173.0869881208 -460.086988120768 56 15594 16382.2063915489 -788.206391548907 57 15683 16487.0999237395 -804.099923739527 58 16438 16769.3387305958 -331.338730595804 59 17032 16800.8611168833 231.138883116751 60 17696 16887.0282757456 808.971724254413

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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