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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: Thu, 13 Dec 2007 04:31:26 -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/Dec/13/t1197544713rd791g0o5l70dwm.htm/, Retrieved Thu, 13 Dec 2007 12:18:43 +0100

User-defined keywords:

Dataseries X:

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106.5 112.3 102.8 96,5 101.0 98.9 105.1 103.0 99.0 104.3 94.6 90.4 108.9 111.4 100.8 102.5 98.2 98.7 113.3 104.6 99.3 111.8 97.3 97.7 115.6 111.9 107.0 107.1 100.6 99.2 108.4 103.0 99.8 115.0 90.8 95.9 114.4 108.2 112.6 109.1 105.0 105.0 118.5 103.7 112.5 116.6 96.6 101.9 116.5 119.3 115.4 108.5 111.5 108.8 121.8 109.6 112.2 119.6 103.4 105.3 113.5

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 industriële_productie[t] = + 98.24 + 14.3266666666667M1[t] + 14.38M2[t] + 9.48M3[t] + 6.49999999999998M4[t] + 5.01999999999999M5[t] + 3.87999999999999M6[t] + 15.18M7[t] + 6.53999999999998M8[t] + 6.31999999999999M9[t] + 15.22M10[t] -1.70000000000001M11[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) 98.24 2.373308 41.3937 0 0 M1 14.3266666666667 3.213475 4.4583 4.8e-05 2.4e-05 M2 14.38 3.356365 4.2844 8.5e-05 4.3e-05 M3 9.48 3.356365 2.8245 0.00683 0.003415 M4 6.49999999999998 3.356365 1.9366 0.05857 0.029285 M5 5.01999999999999 3.356365 1.4957 0.141154 0.070577 M6 3.87999999999999 3.356365 1.156 0.253282 0.126641 M7 15.18 3.356365 4.5227 3.9e-05 1.9e-05 M8 6.53999999999998 3.356365 1.9485 0.057089 0.028545 M9 6.31999999999999 3.356365 1.883 0.065645 0.032823 M10 15.22 3.356365 4.5347 3.7e-05 1.9e-05 M11 -1.70000000000001 3.356365 -0.5065 0.614777 0.307389 Multiple Linear Regression - Regression Statistics Multiple R 0.763493252782389 R-squared 0.582921947044233 Adjusted R-squared 0.489292180054162 F-TEST (value) 6.22581862353725 F-TEST (DF numerator) 11 F-TEST (DF denominator) 49 p-value 2.72441705351234e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.30687911925592 Sum Squared Residuals 1379.98533333333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.5 112.566666666667 -6.0666666666666 2 112.3 112.62 -0.32000000000002 3 102.8 107.72 -4.92000000000001 4 96.5 104.74 -8.24000000000003 5 101 103.26 -2.26000000000001 6 98.9 102.12 -3.22 7 105.1 113.42 -8.32 8 103 104.78 -1.78 9 99 104.56 -5.55999999999999 10 104.3 113.46 -9.15999999999999 11 94.6 96.54 -1.94000000000001 12 90.4 98.24 -7.84 13 108.9 112.566666666667 -3.66666666666668 14 111.4 112.62 -1.21999999999999 15 100.8 107.72 -6.92 16 102.5 104.74 -2.23999999999999 17 98.2 103.26 -5.05999999999999 18 98.7 102.12 -3.41999999999999 19 113.3 113.42 -0.120000000000003 20 104.6 104.78 -0.180000000000005 21 99.3 104.56 -5.26000000000001 22 111.8 113.46 -1.66000000000000 23 97.3 96.54 0.760000000000002 24 97.7 98.24 -0.540000000000003 25 115.6 112.566666666667 3.03333333333331 26 111.9 112.62 -0.719999999999992 27 107 107.72 -0.719999999999991 28 107.1 104.74 2.36000000000001 29 100.6 103.26 -2.66 30 99.2 102.12 -2.92000000000000 31 108.4 113.42 -5.01999999999999 32 103 104.78 -1.78 33 99.8 104.56 -4.76000000000001 34 115 113.46 1.54000000000000 35 90.8 96.54 -5.74 36 95.9 98.24 -2.34 37 114.4 112.566666666667 1.83333333333332 38 108.2 112.62 -4.41999999999999 39 112.6 107.72 4.88 40 109.1 104.74 4.36000000000001 41 105 103.26 1.74000000000001 42 105 102.12 2.88 43 118.5 113.42 5.08 44 103.7 104.78 -1.08000000000000 45 112.5 104.56 7.94 46 116.6 113.46 3.13999999999999 47 96.6 96.54 0.0599999999999987 48 101.9 98.24 3.66 49 116.5 112.566666666667 3.93333333333332 50 119.3 112.62 6.68 51 115.4 107.72 7.68000000000001 52 108.5 104.74 3.76000000000001 53 111.5 103.26 8.24 54 108.8 102.12 6.68 55 121.8 113.42 8.37999999999999 56 109.6 104.78 4.81999999999999 57 112.2 104.56 7.64 58 119.6 113.46 6.14 59 103.4 96.54 6.86000000000001 60 105.3 98.24 7.05999999999999 61 113.5 112.566666666667 0.933333333333317

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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