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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: Fri, 14 Dec 2007 05:38:50 -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/14/t1197635003egfdlqvvfov5stp.htm/, Retrieved Fri, 14 Dec 2007 13:23:24 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

102.7 0 103.2 0 105.6 0 103.9 0 107.2 0 100.7 0 92.1 0 90.3 0 93.4 0 98.5 0 100.8 0 102.3 0 104.7 0 101.1 0 101.4 0 99.5 0 98.4 0 96.3 0 100.7 0 101.2 0 100.3 0 97.8 0 97.4 0 98.6 0 99.7 0 99 0 98.1 0 97 0 98.5 0 103.8 0 114.4 0 124.5 0 134.2 0 131.8 0 125.6 0 119.9 0 114.9 0 115.5 0 112.5 0 111.4 0 115.3 0 110.8 0 103.7 0 111.1 0 113 0 111.2 0 117.6 0 121.7 0 127.3 0 129.8 0 137.1 0 141.4 0 137.4 0 130.7 0 117.2 0 110.8 0 111.4 0 108.2 0 108.8 0 110.2 0 109.5 0 109.5 0 116 0 111.2 0 112.1 0 114 0 119.1 0 114.1 0 115.1 0 115.4 0 110.8 0 116 0 119.2 0 126.5 0 127.8 0 131.3 0 140.3 0 137.3 0 143 0 134.5 0 139.9 1 159.3 1 170.4 1 175 1 175.8 1 180.9 1 180.3 1 169.6 1 172.3 1 184.8 1 177.7 1 184.6 1 211.4 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Graan[t] = + 112.45375 + 63.0847115384616Verandering[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) 112.45375 1.506034 74.6688 0 0 Verandering 63.0847115384616 4.02814 15.661 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.854038451045059 R-squared 0.729381675863443 Adjusted R-squared 0.726407848125679 F-TEST (value) 245.266955648135 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.4703784279265 Sum Squared Residuals 16512.0496442308 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.7 112.45375 -9.75374999999997 2 103.2 112.45375 -9.25375000000008 3 105.6 112.45375 -6.85375 4 103.9 112.45375 -8.55375 5 107.2 112.45375 -5.25375 6 100.7 112.45375 -11.75375 7 92.1 112.45375 -20.35375 8 90.3 112.45375 -22.15375 9 93.4 112.45375 -19.05375 10 98.5 112.45375 -13.95375 11 100.8 112.45375 -11.65375 12 102.3 112.45375 -10.15375 13 104.7 112.45375 -7.75375 14 101.1 112.45375 -11.35375 15 101.4 112.45375 -11.05375 16 99.5 112.45375 -12.95375 17 98.4 112.45375 -14.05375 18 96.3 112.45375 -16.15375 19 100.7 112.45375 -11.75375 20 101.2 112.45375 -11.25375 21 100.3 112.45375 -12.15375 22 97.8 112.45375 -14.65375 23 97.4 112.45375 -15.05375 24 98.6 112.45375 -13.85375 25 99.7 112.45375 -12.75375 26 99 112.45375 -13.45375 27 98.1 112.45375 -14.35375 28 97 112.45375 -15.45375 29 98.5 112.45375 -13.95375 30 103.8 112.45375 -8.65375 31 114.4 112.45375 1.94625000000001 32 124.5 112.45375 12.04625 33 134.2 112.45375 21.74625 34 131.8 112.45375 19.34625 35 125.6 112.45375 13.14625 36 119.9 112.45375 7.44625 37 114.9 112.45375 2.44625000000001 38 115.5 112.45375 3.04625 39 112.5 112.45375 0.0462500000000007 40 111.4 112.45375 -1.05374999999999 41 115.3 112.45375 2.84625 42 110.8 112.45375 -1.65375000000000 43 103.7 112.45375 -8.75375 44 111.1 112.45375 -1.35375000000000 45 113 112.45375 0.546250000000001 46 111.2 112.45375 -1.25375000000000 47 117.6 112.45375 5.14624999999999 48 121.7 112.45375 9.24625 49 127.3 112.45375 14.84625 50 129.8 112.45375 17.34625 51 137.1 112.45375 24.64625 52 141.4 112.45375 28.94625 53 137.4 112.45375 24.94625 54 130.7 112.45375 18.24625 55 117.2 112.45375 4.74625 56 110.8 112.45375 -1.65375000000000 57 111.4 112.45375 -1.05374999999999 58 108.2 112.45375 -4.25375 59 108.8 112.45375 -3.65375 60 110.2 112.45375 -2.25375000000000 61 109.5 112.45375 -2.95375 62 109.5 112.45375 -2.95375 63 116 112.45375 3.54625 64 111.2 112.45375 -1.25375000000000 65 112.1 112.45375 -0.353750000000005 66 114 112.45375 1.54625 67 119.1 112.45375 6.64625 68 114.1 112.45375 1.64624999999999 69 115.1 112.45375 2.64624999999999 70 115.4 112.45375 2.94625000000001 71 110.8 112.45375 -1.65375000000000 72 116 112.45375 3.54625 73 119.2 112.45375 6.74625 74 126.5 112.45375 14.04625 75 127.8 112.45375 15.34625 76 131.3 112.45375 18.84625 77 140.3 112.45375 27.84625 78 137.3 112.45375 24.84625 79 143 112.45375 30.54625 80 134.5 112.45375 22.04625 81 139.9 175.538461538462 -35.6384615384615 82 159.3 175.538461538462 -16.2384615384615 83 170.4 175.538461538462 -5.13846153846154 84 175 175.538461538462 -0.538461538461545 85 175.8 175.538461538462 0.261538461538467 86 180.9 175.538461538462 5.36153846153846 87 180.3 175.538461538462 4.76153846153847 88 169.6 175.538461538462 -5.93846153846155 89 172.3 175.538461538462 -3.23846153846153 90 184.8 175.538461538462 9.26153846153847 91 177.7 175.538461538462 2.16153846153844 92 184.6 175.538461538462 9.06153846153846 93 211.4 175.538461538462 35.8615384615385

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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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Software written by Ed van Stee & Patrick Wessa

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