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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 10:05:20 -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/t11960098162e1egiqe2edvzak.htm/, Retrieved Sun, 25 Nov 2007 17:56:56 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation WLHvrouwen[t] = + 7.83862660944206 + 1.15493562231760x[t] + 0.295171673819742M1[t] + 0.195171673819742M2[t] + 0.0201716738197424M3[t] -0.417328326180258M4[t] -0.542328326180258M5[t] -0.467328326180258M6[t] + 0.532671673819742M7[t] + 0.782671673819742M8[t] + 0.632671673819743M9[t] + 0.493562231759657M10[t] + 1.33118141655746e-16M11[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) 7.83862660944206 0.246876 31.7512 0 0 x 1.15493562231760 0.13994 8.2531 0 0 M1 0.295171673819742 0.295846 0.9977 0.321424 0.160712 M2 0.195171673819742 0.295846 0.6597 0.511337 0.255669 M3 0.0201716738197424 0.295846 0.0682 0.94581 0.472905 M4 -0.417328326180258 0.295846 -1.4106 0.162232 0.081116 M5 -0.542328326180258 0.295846 -1.8331 0.070501 0.035251 M6 -0.467328326180258 0.295846 -1.5796 0.118137 0.059069 M7 0.532671673819742 0.295846 1.8005 0.075551 0.037775 M8 0.782671673819742 0.295846 2.6455 0.009816 0.004908 M9 0.632671673819743 0.295846 2.1385 0.035526 0.017763 M10 0.493562231759657 0.30581 1.6139 0.110476 0.055238 M11 1.33118141655746e-16 0.305156 0 1 0.5 Multiple Linear Regression - Regression Statistics Multiple R 0.77358967571846 R-squared 0.598440986378192 Adjusted R-squared 0.53820713433492 F-TEST (value) 9.93529329567498 F-TEST (DF numerator) 12 F-TEST (DF denominator) 80 p-value 1.440192409774e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.57089514926931 Sum Squared Residuals 26.0737017167382 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.1337982832618 0.566201716738197 2 8.5 8.0337982832618 0.466201716738196 3 8.2 7.8587982832618 0.341201716738197 4 8.3 7.4212982832618 0.878701716738198 5 8 7.2962982832618 0.703701716738198 6 8.1 7.3712982832618 0.728701716738197 7 8.7 8.3712982832618 0.328701716738197 8 9.3 8.6212982832618 0.678701716738198 9 8.9 8.4712982832618 0.428701716738198 10 8.8 8.33218884120172 0.467811158798284 11 8.4 7.83862660944206 0.56137339055794 12 8.4 7.83862660944206 0.56137339055794 13 7.3 8.1337982832618 -0.833798283261802 14 7.2 8.0337982832618 -0.833798283261802 15 7 7.8587982832618 -0.858798283261803 16 7 7.4212982832618 -0.421298283261803 17 6.9 7.2962982832618 -0.396298283261802 18 6.9 7.3712982832618 -0.471298283261802 19 7.1 8.3712982832618 -1.27129828326180 20 7.5 8.6212982832618 -1.12129828326180 21 7.4 8.4712982832618 -1.07129828326180 22 8.9 8.33218884120172 0.567811158798283 23 8.3 8.99356223175966 -0.693562231759656 24 8.3 8.99356223175966 -0.693562231759656 25 9 9.2887339055794 -0.288733905579399 26 8.9 9.1887339055794 -0.288733905579399 27 8.8 9.0137339055794 -0.213733905579399 28 7.8 8.5762339055794 -0.776233905579399 29 7.8 8.4512339055794 -0.651233905579399 30 7.8 8.5262339055794 -0.726233905579399 31 9.2 9.5262339055794 -0.326233905579400 32 9.3 9.7762339055794 -0.476233905579399 33 9.2 9.6262339055794 -0.4262339055794 34 8.6 9.48712446351931 -0.887124463519314 35 8.5 8.99356223175966 -0.493562231759657 36 8.5 8.99356223175966 -0.493562231759657 37 9 9.2887339055794 -0.288733905579399 38 9 9.1887339055794 -0.188733905579399 39 8.8 9.0137339055794 -0.213733905579399 40 8 8.5762339055794 -0.576233905579399 41 7.9 8.4512339055794 -0.551233905579399 42 8.1 8.5262339055794 -0.426233905579399 43 9.3 9.5262339055794 -0.226233905579398 44 9.4 9.7762339055794 -0.376233905579399 45 9.4 9.6262339055794 -0.226233905579399 46 9.3 9.48712446351931 -0.187124463519313 47 9 8.99356223175966 0.00643776824034309 48 9.1 8.99356223175966 0.106437768240343 49 9.7 9.2887339055794 0.4112660944206 50 9.7 9.1887339055794 0.5112660944206 51 9.6 9.0137339055794 0.5862660944206 52 8.3 8.5762339055794 -0.276233905579399 53 8.2 8.4512339055794 -0.2512339055794 54 8.4 8.5262339055794 -0.126233905579399 55 10.6 9.5262339055794 1.0737660944206 56 10.9 9.7762339055794 1.1237660944206 57 10.9 9.6262339055794 1.2737660944206 58 9.6 9.48712446351931 0.112875536480686 59 9.3 8.99356223175966 0.306437768240344 60 9.3 8.99356223175966 0.306437768240344 61 9.6 9.2887339055794 0.311266094420601 62 9.5 9.1887339055794 0.311266094420601 63 9.5 9.0137339055794 0.486266094420601 64 9 8.5762339055794 0.423766094420601 65 8.9 8.4512339055794 0.448766094420601 66 9 8.5262339055794 0.473766094420601 67 10.1 9.5262339055794 0.573766094420601 68 10.2 9.7762339055794 0.4237660944206 69 10.2 9.6262339055794 0.5737660944206 70 9.5 9.48712446351931 0.0128755364806864 71 9.3 8.99356223175966 0.306437768240344 72 9.3 8.99356223175966 0.306437768240344 73 9.4 9.2887339055794 0.111266094420601 74 9.3 9.1887339055794 0.111266094420601 75 9.1 9.0137339055794 0.0862660944206004 76 9 8.5762339055794 0.423766094420601 77 8.9 8.4512339055794 0.448766094420601 78 9 8.5262339055794 0.473766094420601 79 9.8 9.5262339055794 0.273766094420602 80 10 9.7762339055794 0.223766094420601 81 9.8 9.6262339055794 0.173766094420601 82 9.4 9.48712446351931 -0.0871244635193132 83 9 8.99356223175966 0.00643776824034309 84 8.9 8.99356223175966 -0.0935622317596566 85 9.3 9.2887339055794 0.0112660944206016 86 9.1 9.1887339055794 -0.0887339055793996 87 8.8 9.0137339055794 -0.213733905579399 88 8.9 8.5762339055794 0.323766094420601 89 8.7 8.4512339055794 0.2487660944206 90 8.6 8.5262339055794 0.0737660944206005 91 9.1 9.5262339055794 -0.426233905579399 92 9.3 9.7762339055794 -0.476233905579399 93 8.9 9.6262339055794 -0.726233905579399

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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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Software written by Ed van Stee & Patrick Wessa

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