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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 09:59:13 -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/t1196009479zfyhlg734xzmdh7.htm/, Retrieved Sun, 25 Nov 2007 17:51:29 +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] = + 7.97727272727272 + 1.13822023047375x[t] + 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) 7.97727272727272 0.146848 54.3235 0 0 x 1.13822023047375 0.168066 6.7725 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.578893514173126 R-squared 0.335117700751711 Adjusted R-squared 0.327811301858873 F-TEST (value) 45.8663297291626 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 1.21531473773473e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.688776540025267 Sum Squared Residuals 43.1715941101152 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 7.97727272727275 0.722727272727247 2 8.5 7.97727272727272 0.522727272727278 3 8.2 7.97727272727273 0.222727272727273 4 8.3 7.97727272727273 0.322727272727274 5 8 7.97727272727273 0.0227272727272737 6 8.1 7.97727272727273 0.122727272727273 7 8.7 7.97727272727273 0.722727272727273 8 9.3 7.97727272727273 1.32272727272727 9 8.9 7.97727272727273 0.922727272727274 10 8.8 7.97727272727273 0.822727272727274 11 8.4 7.97727272727273 0.422727272727274 12 8.4 7.97727272727273 0.422727272727274 13 7.3 7.97727272727273 -0.677272727272726 14 7.2 7.97727272727273 -0.777272727272726 15 7 7.97727272727273 -0.977272727272726 16 7 7.97727272727273 -0.977272727272726 17 6.9 7.97727272727273 -1.07727272727273 18 6.9 7.97727272727273 -1.07727272727273 19 7.1 7.97727272727273 -0.877272727272727 20 7.5 7.97727272727273 -0.477272727272726 21 7.4 7.97727272727273 -0.577272727272726 22 8.9 7.97727272727273 0.922727272727274 23 8.3 9.11549295774648 -0.815492957746478 24 8.3 9.11549295774648 -0.815492957746478 25 9 9.11549295774648 -0.115492957746479 26 8.9 9.11549295774648 -0.215492957746479 27 8.8 9.11549295774648 -0.315492957746478 28 7.8 9.11549295774648 -1.31549295774648 29 7.8 9.11549295774648 -1.31549295774648 30 7.8 9.11549295774648 -1.31549295774648 31 9.2 9.11549295774648 0.0845070422535203 32 9.3 9.11549295774648 0.184507042253522 33 9.2 9.11549295774648 0.0845070422535203 34 8.6 9.11549295774648 -0.51549295774648 35 8.5 9.11549295774648 -0.615492957746479 36 8.5 9.11549295774648 -0.615492957746479 37 9 9.11549295774648 -0.115492957746479 38 9 9.11549295774648 -0.115492957746479 39 8.8 9.11549295774648 -0.315492957746478 40 8 9.11549295774648 -1.11549295774648 41 7.9 9.11549295774648 -1.21549295774648 42 8.1 9.11549295774648 -1.01549295774648 43 9.3 9.11549295774648 0.184507042253522 44 9.4 9.11549295774648 0.284507042253521 45 9.4 9.11549295774648 0.284507042253521 46 9.3 9.11549295774648 0.184507042253522 47 9 9.11549295774648 -0.115492957746479 48 9.1 9.11549295774648 -0.0154929577464794 49 9.7 9.11549295774648 0.58450704225352 50 9.7 9.11549295774648 0.58450704225352 51 9.6 9.11549295774648 0.48450704225352 52 8.3 9.11549295774648 -0.815492957746478 53 8.2 9.11549295774648 -0.91549295774648 54 8.4 9.11549295774648 -0.715492957746479 55 10.6 9.11549295774648 1.48450704225352 56 10.9 9.11549295774648 1.78450704225352 57 10.9 9.11549295774648 1.78450704225352 58 9.6 9.11549295774648 0.48450704225352 59 9.3 9.11549295774648 0.184507042253522 60 9.3 9.11549295774648 0.184507042253522 61 9.6 9.11549295774648 0.48450704225352 62 9.5 9.11549295774648 0.384507042253521 63 9.5 9.11549295774648 0.384507042253521 64 9 9.11549295774648 -0.115492957746479 65 8.9 9.11549295774648 -0.215492957746479 66 9 9.11549295774648 -0.115492957746479 67 10.1 9.11549295774648 0.98450704225352 68 10.2 9.11549295774648 1.08450704225352 69 10.2 9.11549295774648 1.08450704225352 70 9.5 9.11549295774648 0.384507042253521 71 9.3 9.11549295774648 0.184507042253522 72 9.3 9.11549295774648 0.184507042253522 73 9.4 9.11549295774648 0.284507042253521 74 9.3 9.11549295774648 0.184507042253522 75 9.1 9.11549295774648 -0.0154929577464794 76 9 9.11549295774648 -0.115492957746479 77 8.9 9.11549295774648 -0.215492957746479 78 9 9.11549295774648 -0.115492957746479 79 9.8 9.11549295774648 0.684507042253522 80 10 9.11549295774648 0.884507042253521 81 9.8 9.11549295774648 0.684507042253522 82 9.4 9.11549295774648 0.284507042253521 83 9 9.11549295774648 -0.115492957746479 84 8.9 9.11549295774648 -0.215492957746479 85 9.3 9.11549295774648 0.184507042253522 86 9.1 9.11549295774648 -0.0154929577464794 87 8.8 9.11549295774648 -0.315492957746478 88 8.9 9.11549295774648 -0.215492957746479 89 8.7 9.11549295774648 -0.41549295774648 90 8.6 9.11549295774648 -0.51549295774648 91 9.1 9.11549295774648 -0.0154929577464794 92 9.3 9.11549295774648 0.184507042253522 93 8.9 9.11549295774648 -0.215492957746479

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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