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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, 18 Nov 2007 13:27:47 -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/18/t1195417275lep30mplchkm4w2.htm/, Retrieved Sun, 18 Nov 2007 21:21:25 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

6,4 8,7 0 6,3 8,5 0 6 8,2 0 5,3 8,3 0 5,2 8 0 5,1 8,1 0 5,4 8,7 0 5,8 9,3 0 5,6 8,9 0 5,6 8,8 0 5,4 8,4 0 5,4 8,4 0 5,5 7,3 0 5,5 7,2 0 5,3 7 0 5,7 7 0 5,6 6,9 0 5,5 6,9 0 5,6 7,1 0 5,9 7,5 0 6 7,4 0 7 8,9 0 6,6 8,3 1 6,6 8,3 0 6,3 9 0 6,3 8,9 0 6,3 8,8 0 6,3 7,8 0 6,2 7,8 0 6,2 7,8 0 6,3 9,2 0 6,4 9,3 0 6,4 9,2 0 7,8 8,6 0 7,7 8,5 0 7,7 8,5 0 7,7 9 0 7,7 9 0 7,6 8,8 0 7,5 8 0 7,4 7,9 0 7,4 8,1 0 7,5 9,3 0 7,6 9,4 0 7,6 9,4 0 8,1 9,3 1 7,8 9 0 8 9,1 0 7,9 9,7 0 7,9 9,7 0 7,8 9,6 0 6,7 8,3 0 6,6 8,2 0 6,6 8,4 0 7,7 10,6 0 7,9 10,9 0 8 10,9 0 7,7 9,6 0 7,5 9,3 0 7,6 9,3 0 7,8 9,6 0 7,8 9,5 0 7,7 9,5 0 7,4 9 0 7,5 8,9 0 7,2 9 0 7,5 10,1 0 7,6 10,2 0 7,6 10,2 0 7,8 9,5 0 7,7 9,3 0 7,7 9,3 0 8,2 9,4 0 8,2 9,3 0 8,1 9,1 0 7,8 9 0 7,8 8,9 0 7,7 9 0 6,7 9,8 0 6,7 10 0 6,7 9,8 0 7,2 9,4 0 6,9 9 1 6,8 8,9 0 7,2 9,3 0 7,1 9,1 0 6,9 8,8 0 6,9 8,9 1 6,7 8,7 0 6,5 8,6 0 6,6 9,1 0 6,6 9,3 0 6,5 8,9 0

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 M[t] = + 0.8414664187967 + 0.683065915557792V[t] + 0.221323580627898x[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) 0.8414664187967 0.74177 1.1344 0.259638 0.129819 V 0.683065915557792 0.083475 8.1828 0 0 x 0.221323580627898 0.343797 0.6438 0.521366 0.260683 Multiple Linear Regression - Regression Statistics Multiple R 0.654525601329131 R-squared 0.428403762795261 Adjusted R-squared 0.415701624190711 F-TEST (value) 33.7269003380117 F-TEST (DF numerator) 2 F-TEST (DF denominator) 90 p-value 1.17225118501096e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.672625893279218 Sum Squared Residuals 40.71830330787 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.4 6.78413988414947 -0.384139884149473 2 6.3 6.64752670103793 -0.347526701037931 3 6 6.44260692637059 -0.442606926370593 4 5.3 6.51091351792637 -1.21091351792637 5 5.2 6.30599374325903 -1.10599374325903 6 5.1 6.37430033481481 -1.27430033481481 7 5.4 6.78413988414949 -1.38413988414949 8 5.8 7.19397943348416 -1.39397943348416 9 5.6 6.92075306726105 -1.32075306726105 10 5.6 6.85244647570527 -1.25244647570527 11 5.4 6.57922010948215 -1.17922010948215 12 5.4 6.57922010948215 -1.17922010948215 13 5.5 5.82784760236858 -0.32784760236858 14 5.5 5.7595410108128 -0.259541010812801 15 5.3 5.62292782770124 -0.322927827701243 16 5.7 5.62292782770124 0.0770721722987576 17 5.6 5.55462123614546 0.0453787638545361 18 5.5 5.55462123614546 -0.0546212361454636 19 5.6 5.69123441925702 -0.091234419257022 20 5.9 5.96446078548014 -0.0644607854801381 21 6 5.89615419392436 0.103845806075641 22 7 6.92075306726105 0.0792469327389527 23 6.6 6.73223709855427 -0.132237098554270 24 6.6 6.51091351792637 0.0890864820736272 25 6.3 6.98905965881683 -0.689059658816826 26 6.3 6.92075306726105 -0.620753067261047 27 6.3 6.85244647570527 -0.552446475705269 28 6.3 6.16938056014748 0.130619439852524 29 6.2 6.16938056014748 0.0306194398525243 30 6.2 6.16938056014748 0.0306194398525243 31 6.3 7.12567284192838 -0.825672841928384 32 6.4 7.19397943348416 -0.793979433484164 33 6.4 7.12567284192838 -0.725672841928384 34 7.8 6.71583329259371 1.08416670740629 35 7.7 6.64752670103793 1.05247329896207 36 7.7 6.64752670103793 1.05247329896207 37 7.7 6.98905965881683 0.710940341183174 38 7.7 6.98905965881683 0.710940341183174 39 7.6 6.85244647570527 0.747553524294731 40 7.5 6.30599374325903 1.19400625674097 41 7.4 6.23768715170326 1.16231284829675 42 7.4 6.37430033481481 1.02569966518519 43 7.5 7.19397943348416 0.306020566515836 44 7.6 7.26228602503994 0.337713974960056 45 7.6 7.26228602503994 0.337713974960056 46 8.1 7.41530301411206 0.684696985887938 47 7.8 6.98905965881683 0.810940341183174 48 8 7.0573662503726 0.942633749627395 49 7.9 7.46720579970728 0.43279420029272 50 7.9 7.46720579970728 0.43279420029272 51 7.8 7.3988992081515 0.401100791848499 52 6.7 6.51091351792637 0.189086482073628 53 6.6 6.44260692637059 0.157393073629407 54 6.6 6.57922010948215 0.0207798905178482 55 7.7 8.0819651237093 -0.381965123709293 56 7.9 8.28688489837663 -0.386884898376630 57 8 8.28688489837663 -0.286884898376631 58 7.7 7.3988992081515 0.301100791848499 59 7.5 7.19397943348416 0.306020566515836 60 7.6 7.19397943348416 0.406020566515835 61 7.8 7.3988992081515 0.401100791848499 62 7.8 7.33059261659572 0.469407383404278 63 7.7 7.33059261659572 0.369407383404278 64 7.4 6.98905965881683 0.410940341183174 65 7.5 6.92075306726105 0.579246932738953 66 7.2 6.98905965881683 0.210940341183174 67 7.5 7.7404321659304 -0.240432165930397 68 7.6 7.80873875748618 -0.208738757486176 69 7.6 7.80873875748618 -0.208738757486176 70 7.8 7.33059261659572 0.469407383404278 71 7.7 7.19397943348416 0.506020566515836 72 7.7 7.19397943348416 0.506020566515836 73 8.2 7.26228602503994 0.937713974960056 74 8.2 7.19397943348416 1.00602056651584 75 8.1 7.0573662503726 1.04263374962739 76 7.8 6.98905965881683 0.810940341183174 77 7.8 6.92075306726105 0.879246932738953 78 7.7 6.98905965881683 0.710940341183174 79 6.7 7.53551239126306 -0.83551239126306 80 6.7 7.67212557437462 -0.972125574374618 81 6.7 7.53551239126306 -0.83551239126306 82 7.2 7.26228602503994 -0.062286025039943 83 6.9 7.21038323944472 -0.310383239444723 84 6.8 6.92075306726105 -0.120753067261047 85 7.2 7.19397943348416 0.00602056651583593 86 7.1 7.0573662503726 0.0426337496273944 87 6.9 6.85244647570527 0.047553524294732 88 6.9 7.14207664788894 -0.242076647888944 89 6.7 6.78413988414949 -0.084139884149488 90 6.5 6.71583329259371 -0.215833292593709 91 6.6 7.0573662503726 -0.457366250372606 92 6.6 7.19397943348416 -0.593979433484165 93 6.5 6.92075306726105 -0.420753067261047

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')

Copyright

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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