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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 15:59:35 -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/t1195512742bab6kv036xhlsr8.htm/, Retrieved Mon, 19 Nov 2007 23:52:23 +0100

User-defined keywords:

Dataseries X:

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99.5 0 101.6 0 103.9 0 106.6 0 108.3 0 102 0 93.8 0 91.6 0 97.7 0 94.8 0 98 0 103.8 0 97.8 0 91.2 0 89.3 0 87.5 0 90.4 0 94.2 0 102.2 0 101.3 0 96 0 90.8 0 93.2 0 90.9 0 91.1 0 90.2 0 94.3 0 96 0 99 0 103.3 0 113.1 0 112.8 0 112.1 0 107.4 0 111 0 110.5 0 110.8 0 112.4 0 111.5 0 116.2 0 122.5 0 121.3 0 113.9 0 110.7 0 120.8 0 141.1 1 147.4 1 148 1 158.1 1 165 1 187 1 190.3 1 182.4 1 168.8 1 151.2 1 120.1 1 112.5 1 106.2 1 107.1 1 108.5 1 106.5 1 108.3 1 125.6 1 124 1 127.2 1 136.9 1 135.8 1 124.3 1 115.4 1 113.6 1 114.4 1 118.4 1 117 1 116.5 1 115.4 1 113.6 1 117.4 1 116.9 1 116.4 1 111.1 1 110.2 1 118.9 1 131.8 1 130.6 1 138.3 1 148.4 1 148.7 1 144.3 1 152.5 1 162.9 1 167.2 1 166.5 1 185.6 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 Y[t] = + 102.384444444444 + 32.4968055555556x[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) 102.384444444444 2.792319 36.6665 0 0 x 32.4968055555556 3.886744 8.3609 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.65912788091277 R-squared 0.434449563396558 Adjusted R-squared 0.428234723433883 F-TEST (value) 69.9051891932465 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 6.82010004027234e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18.7314486206965 Sum Squared Residuals 31928.9122361111 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.5 102.384444444444 -2.8844444444445 2 101.6 102.384444444444 -0.784444444444432 3 103.9 102.384444444444 1.51555555555556 4 106.6 102.384444444444 4.21555555555555 5 108.3 102.384444444444 5.91555555555555 6 102 102.384444444444 -0.384444444444442 7 93.8 102.384444444444 -8.58444444444445 8 91.6 102.384444444444 -10.7844444444445 9 97.7 102.384444444444 -4.68444444444444 10 94.8 102.384444444444 -7.58444444444445 11 98 102.384444444444 -4.38444444444444 12 103.8 102.384444444444 1.41555555555555 13 97.8 102.384444444444 -4.58444444444445 14 91.2 102.384444444444 -11.1844444444444 15 89.3 102.384444444444 -13.0844444444444 16 87.5 102.384444444444 -14.8844444444444 17 90.4 102.384444444444 -11.9844444444444 18 94.2 102.384444444444 -8.18444444444444 19 102.2 102.384444444444 -0.184444444444440 20 101.3 102.384444444444 -1.08444444444445 21 96 102.384444444444 -6.38444444444444 22 90.8 102.384444444444 -11.5844444444444 23 93.2 102.384444444444 -9.18444444444444 24 90.9 102.384444444444 -11.4844444444444 25 91.1 102.384444444444 -11.2844444444445 26 90.2 102.384444444444 -12.1844444444444 27 94.3 102.384444444444 -8.08444444444445 28 96 102.384444444444 -6.38444444444444 29 99 102.384444444444 -3.38444444444444 30 103.3 102.384444444444 0.915555555555555 31 113.1 102.384444444444 10.7155555555556 32 112.8 102.384444444444 10.4155555555556 33 112.1 102.384444444444 9.71555555555555 34 107.4 102.384444444444 5.01555555555556 35 111 102.384444444444 8.61555555555556 36 110.5 102.384444444444 8.11555555555556 37 110.8 102.384444444444 8.41555555555555 38 112.4 102.384444444444 10.0155555555556 39 111.5 102.384444444444 9.11555555555556 40 116.2 102.384444444444 13.8155555555556 41 122.5 102.384444444444 20.1155555555556 42 121.3 102.384444444444 18.9155555555556 43 113.9 102.384444444444 11.5155555555556 44 110.7 102.384444444444 8.31555555555556 45 120.8 102.384444444444 18.4155555555556 46 141.1 134.88125 6.21874999999999 47 147.4 134.88125 12.51875 48 148 134.88125 13.11875 49 158.1 134.88125 23.21875 50 165 134.88125 30.11875 51 187 134.88125 52.11875 52 190.3 134.88125 55.41875 53 182.4 134.88125 47.51875 54 168.8 134.88125 33.91875 55 151.2 134.88125 16.31875 56 120.1 134.88125 -14.78125 57 112.5 134.88125 -22.38125 58 106.2 134.88125 -28.68125 59 107.1 134.88125 -27.78125 60 108.5 134.88125 -26.38125 61 106.5 134.88125 -28.38125 62 108.3 134.88125 -26.58125 63 125.6 134.88125 -9.28125 64 124 134.88125 -10.88125 65 127.2 134.88125 -7.68125 66 136.9 134.88125 2.01875000000000 67 135.8 134.88125 0.918750000000009 68 124.3 134.88125 -10.58125 69 115.4 134.88125 -19.48125 70 113.6 134.88125 -21.28125 71 114.4 134.88125 -20.48125 72 118.4 134.88125 -16.48125 73 117 134.88125 -17.88125 74 116.5 134.88125 -18.38125 75 115.4 134.88125 -19.48125 76 113.6 134.88125 -21.28125 77 117.4 134.88125 -17.48125 78 116.9 134.88125 -17.98125 79 116.4 134.88125 -18.48125 80 111.1 134.88125 -23.78125 81 110.2 134.88125 -24.68125 82 118.9 134.88125 -15.98125 83 131.8 134.88125 -3.08124999999999 84 130.6 134.88125 -4.28125000000001 85 138.3 134.88125 3.41875000000001 86 148.4 134.88125 13.51875 87 148.7 134.88125 13.8187500000000 88 144.3 134.88125 9.41875 89 152.5 134.88125 17.61875 90 162.9 134.88125 28.01875 91 167.2 134.88125 32.31875 92 166.5 134.88125 31.61875 93 185.6 134.88125 50.71875

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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