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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: Mon, 19 Nov 2007 03:58:58 -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/19/t1195469844tv6bdcb7qb9wd64.htm/, Retrieved Mon, 19 Nov 2007 11:57:24 +0100

User-defined keywords:

Dataseries X:

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8,5 0 8,6 0 8,5 0 8,5 0 9 0 9 0 8,8 0 8 0 7,9 0 8,1 0 9,3 0 9,4 0 9,4 0 9,3 0 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 10 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 9.57547231270359 + 1.04177524429967x[t] -0.266776149113282M1[t] -0.59633731451321M2[t] -1.05222312703583M3[t] -1.03975389069852M4[t] -0.647284654361202M5[t] -0.714815418023887M6[t] -0.862346181686573M7[t] -1.36987694534926M8[t] -1.47740770901194M9[t] -1.36493847267463M10[t] -0.192469236337315M11[t] -0.0124692363373145t + 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) 9.57547231270359 0.189209 50.6078 0 0 x 1.04177524429967 0.164053 6.3502 0 0 M1 -0.266776149113282 0.218526 -1.2208 0.228252 0.114126 M2 -0.59633731451321 0.229267 -2.6011 0.012387 0.006193 M3 -1.05222312703583 0.23042 -4.5665 3.6e-05 1.8e-05 M4 -1.03975389069852 0.22985 -4.5236 4.1e-05 2.1e-05 M5 -0.647284654361202 0.229345 -2.8223 0.006967 0.003484 M6 -0.714815418023887 0.228907 -3.1227 0.003064 0.001532 M7 -0.862346181686573 0.228536 -3.7733 0.000451 0.000225 M8 -1.36987694534926 0.228232 -6.0021 0 0 M9 -1.47740770901194 0.227995 -6.48 0 0 M10 -1.36493847267463 0.227826 -5.9912 0 0 M11 -0.192469236337315 0.227724 -0.8452 0.402289 0.201144 t -0.0124692363373145 0.003929 -3.1733 0.002657 0.001329 Multiple Linear Regression - Regression Statistics Multiple R 0.86239729601255 R-squared 0.743729096169758 Adjusted R-squared 0.672845654684797 F-TEST (value) 10.4922825499035 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 6.5846827990157e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.360009378495489 Sum Squared Residuals 6.09151737242127 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.5 9.29622692725298 -0.796226927252981 2 8.6 8.95419652551574 -0.354196525515745 3 8.5 8.48584147665581 0.0141585233441906 4 8.5 8.48584147665581 0.0141585233441908 5 9 8.86584147665581 0.134158523344190 6 9 8.78584147665581 0.214158523344191 7 8.8 8.62584147665581 0.174158523344192 8 8 8.10584147665581 -0.105841476655810 9 7.9 7.98584147665581 -0.085841476655809 10 8.1 8.08584147665581 0.0141585233441907 11 9.3 9.24584147665581 0.0541585233441909 12 9.4 9.42584147665581 -0.0258414766558089 13 9.4 9.14659609120521 0.253403908794787 14 9.3 8.80456568946797 0.495434310532031 15 9 9.3779858849077 -0.377985884907709 16 9.1 9.3779858849077 -0.277985884907710 17 9.7 9.7579858849077 -0.0579858849077093 18 9.7 9.6779858849077 0.0220141150922907 19 9.6 9.5179858849077 0.0820141150922907 20 8.3 8.99798588490771 -0.697985884907708 21 8.2 8.8779858849077 -0.67798588490771 22 8.4 8.9779858849077 -0.577985884907708 23 10.6 10.1379858849077 0.462014115092291 24 10.9 10.3179858849077 0.582014115092291 25 10.9 10.0387404994571 0.861259500542887 26 9.6 9.69671009771987 -0.0967100977198696 27 9.3 9.22835504885994 0.0716449511400656 28 9.3 9.22835504885994 0.0716449511400656 29 9.6 9.60835504885993 -0.00835504885993503 30 9.5 9.52835504885993 -0.0283550488599347 31 9.5 9.36835504885993 0.131644951140065 32 9 8.84835504885993 0.151644951140065 33 8.9 8.72835504885994 0.171644951140066 34 9 8.82835504885993 0.171644951140065 35 10.1 9.98835504885994 0.111644951140065 36 10.2 10.1683550488599 0.0316449511400643 37 10.2 9.88910966340934 0.310890336590661 38 9.5 9.5470792616721 -0.0470792616720952 39 9.3 9.07872421281216 0.22127578718784 40 9.3 9.07872421281216 0.221275787187840 41 9.4 9.45872421281216 -0.0587242128121602 42 9.3 9.37872421281216 -0.0787242128121599 43 9.1 9.21872421281216 -0.118724212812161 44 9 8.69872421281216 0.301275787187839 45 8.9 8.57872421281216 0.32127578718784 46 9 8.67872421281216 0.321275787187839 47 9.8 9.83872421281216 -0.0387242128121598 48 10 10.0187242128122 -0.0187242128121607 49 9.8 9.73947882736156 0.0605211726384363 50 9.4 9.39744842562432 0.00255157437567918 51 9 8.92909337676439 0.070906623235613 52 8.9 8.92909337676439 -0.0290933767643866 53 9.3 9.30909337676439 -0.00909337676438587 54 9.1 9.22909337676439 -0.129093376764387 55 8.8 9.06909337676439 -0.269093376764386 56 8.9 8.54909337676439 0.350906623235614 57 8.7 8.42909337676439 0.270906623235613 58 8.6 8.52909337676439 0.0709066232356131 59 9.1 9.68909337676439 -0.589093376764387 60 9.3 9.86909337676439 -0.569093376764386 61 8.9 9.5898479913138 -0.68984799131379

Charts produced by software:

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Parameters:

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')

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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