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Paper: multiple lineair regression: LT

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 12 Dec 2007 03:31:16 -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/12/t1197454584vspw27zldd3cakz.htm/, Retrieved Wed, 12 Dec 2007 11:16:34 +0100

User-defined keywords:

Dataseries X:

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0.9383 0 0.9217 0 0.9095 0 0.8920 0 0.8742 0 0.8532 0 0.8607 0 0.9005 0 0.9111 0 0.9059 0 0.8883 0 0.8924 0 0.8833 1 0.8700 1 0.8758 1 0.8858 1 0.9170 1 0.9554 1 0.9922 1 0.9778 1 0.9808 1 0.9811 1 1.0014 1 1.0183 1 1.0622 1 1.0773 1 1.0807 1 1.0848 1 1.1582 1 1.1663 1 1.1372 1 1.1139 1 1.1222 1 1.1692 1 1.1702 1 1.2286 1 1.2613 1 1.2646 1 1.2262 1 1.1985 1 1.2007 1 1.2138 1 1.2266 1 1.2176 1 1.2218 1 1.2490 1 1.2991 1 1.3408 1 1.3119 1 1.3014 1 1.3201 1 1.2938 1 1.2694 1 1.2165 1 1.2037 1 1.2292 1 1.2256 1 1.2015 1 1.1786 1 1.1856 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.835673333333333 -0.00767916666666667x[t] + 0.0510297222222221M1[t] + 0.0381961111111111M2[t] + 0.0252225000000000M3[t] + 0.00530888888888889M4[t] + 0.00979527777777786M5[t] -0.0014983333333333M6[t] -0.00689194444444443M7[t] -0.0116055555555555M8[t] -0.0155391666666666M9[t] -0.0149327777777777M10[t] -0.0171863888888889M11[t] + 0.00843361111111111t + 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) 0.835673333333333 0.035511 23.5329 0 0 x -0.00767916666666667 0.03045 -0.2522 0.80202 0.40101 M1 0.0510297222222221 0.042925 1.1888 0.240619 0.12031 M2 0.0381961111111111 0.042799 0.8924 0.376797 0.188399 M3 0.0252225000000000 0.042685 0.5909 0.557478 0.278739 M4 0.00530888888888889 0.042582 0.1247 0.901325 0.450662 M5 0.00979527777777786 0.042491 0.2305 0.818706 0.409353 M6 -0.0014983333333333 0.042412 -0.0353 0.971971 0.485986 M7 -0.00689194444444443 0.042345 -0.1628 0.871424 0.435712 M8 -0.0116055555555555 0.042291 -0.2744 0.784988 0.392494 M9 -0.0155391666666666 0.042248 -0.3678 0.714703 0.357352 M10 -0.0149327777777777 0.042218 -0.3537 0.725172 0.362586 M11 -0.0171863888888889 0.042199 -0.4073 0.6857 0.34285 t 0.00843361111111111 0.000718 11.7506 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.924625433482215 R-squared 0.854932192242175 Adjusted R-squared 0.813934768310616 F-TEST (value) 20.8533149221617 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.9960036108132e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0667132036938824 Sum Squared Residuals 0.204729971166667 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.9383 0.895136666666667 0.0431633333333327 2 0.9217 0.890736666666667 0.0309633333333334 3 0.9095 0.886196666666667 0.0233033333333334 4 0.892 0.874716666666667 0.0172833333333334 5 0.8742 0.887636666666667 -0.0134366666666666 6 0.8532 0.884776666666667 -0.0315766666666665 7 0.8607 0.887816666666667 -0.0271166666666665 8 0.9005 0.891536666666667 0.00896333333333335 9 0.9111 0.896036666666667 0.0150633333333334 10 0.9059 0.905076666666667 0.000823333333333425 11 0.8883 0.911256666666666 -0.0229566666666666 12 0.8924 0.936876666666667 -0.0444766666666666 13 0.8833 0.988660833333333 -0.105360833333333 14 0.87 0.984260833333333 -0.114260833333333 15 0.8758 0.979720833333333 -0.103920833333333 16 0.8858 0.968240833333333 -0.0824408333333334 17 0.917 0.981160833333333 -0.0641608333333333 18 0.9554 0.978300833333333 -0.0229008333333333 19 0.9922 0.981340833333333 0.0108591666666667 20 0.9778 0.985060833333333 -0.00726083333333333 21 0.9808 0.989560833333333 -0.00876083333333336 22 0.9811 0.998600833333333 -0.0175008333333334 23 1.0014 1.00478083333333 -0.00338083333333326 24 1.0183 1.03040083333333 -0.0121008333333333 25 1.0622 1.08986416666667 -0.0276641666666665 26 1.0773 1.08546416666667 -0.00816416666666668 27 1.0807 1.08092416666667 -0.000224166666666679 28 1.0848 1.06944416666667 0.0153558333333333 29 1.1582 1.08236416666667 0.0758358333333332 30 1.1663 1.07950416666667 0.0867958333333332 31 1.1372 1.08254416666667 0.0546558333333333 32 1.1139 1.08626416666667 0.0276358333333332 33 1.1222 1.09076416666667 0.0314358333333334 34 1.1692 1.09980416666667 0.0693958333333333 35 1.1702 1.10598416666667 0.0642158333333332 36 1.2286 1.13160416666667 0.0969958333333333 37 1.2613 1.1910675 0.0702325000000002 38 1.2646 1.1866675 0.0779325 39 1.2262 1.1821275 0.0440724999999999 40 1.1985 1.1706475 0.0278524999999999 41 1.2007 1.1835675 0.0171325000000001 42 1.2138 1.1807075 0.0330925 43 1.2266 1.1837475 0.0428524999999999 44 1.2176 1.1874675 0.0301325 45 1.2218 1.1919675 0.0298324999999999 46 1.249 1.2010075 0.0479925000000001 47 1.2991 1.2071875 0.0919124999999999 48 1.3408 1.2328075 0.1079925 49 1.3119 1.29227083333333 0.0196291666666669 50 1.3014 1.28787083333333 0.0135291666666666 51 1.3201 1.28333083333333 0.0367691666666667 52 1.2938 1.27185083333333 0.0219491666666668 53 1.2694 1.28477083333333 -0.0153708333333333 54 1.2165 1.28191083333333 -0.0654108333333334 55 1.2037 1.28495083333333 -0.0812508333333334 56 1.2292 1.28867083333333 -0.0594708333333333 57 1.2256 1.29317083333333 -0.0675708333333334 58 1.2015 1.30221083333333 -0.100710833333333 59 1.1786 1.30839083333333 -0.129790833333333 60 1.1856 1.33401083333333 -0.148410833333333

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')

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Software written by Ed van Stee & Patrick Wessa

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