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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, 30 Nov 2007 04:09:54 -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/30/t1196420420msqbtshj6knl0g0.htm/, Retrieved Fri, 30 Nov 2007 12:00:21 +0100

User-defined keywords:

Dataseries X:

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106,7 0 110,2 0 125,9 0 100,1 0 106,4 0 114,8 0 81,3 0 87 0 104,2 0 108 0 105 0 94,5 0 92 0 95,9 0 108,8 0 103,4 0 102,1 0 110,1 0 83,2 0 82,7 0 106,8 0 113,7 0 102,5 0 96,6 0 92,1 0 95,6 0 102,3 0 98,6 0 98,2 0 104,5 0 84 0 73,8 0 103,9 0 106 0 97,2 0 102,6 0 89 0 93,8 0 116,7 1 106,8 1 98,5 1 118,7 1 90 1 91,9 1 113,3 1 113,1 1 104,1 1 108,7 1 96,7 1 101 1 116,9 1 105,8 1 99 1 129,4 1 83 1 88,9 1 115,9 1 104,2 1 113,4 1 112,2 1 100,8 1 107,3 1 126,6 1 102,9 1 117,9 1 128,8 1 87,5 1 93,8 1 122,7 1 126,2 1 124,6 1 116,7 1 115,2 1 111,1 1 129,9 1 113,3 1 118,5 1 133,5 1 102,1 1 102,4 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 y[t] = + 100.102717391304 + 10.2278985507246x[t] -5.55753105590065M1[t] -2.35753105590062M2[t] + 12.2099120082816M3[t] -1.53294513457557M4[t] -0.147230848861288M5[t] + 14.0241977225673M6[t] -18.6472308488613M7[t] -17.3043737060041M8[t] + 5.91666666666667M9[t] + 6.65M10[t] + 2.58333333333333M11[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) 100.102717391304 2.830851 35.3613 0 0 x 10.2278985507246 1.505492 6.7937 0 0 M1 -5.55753105590065 3.720467 -1.4938 0.13993 0.069965 M2 -2.35753105590062 3.720467 -0.6337 0.528457 0.264228 M3 12.2099120082816 3.720467 3.2818 0.00164 0.00082 M4 -1.53294513457557 3.720467 -0.412 0.681633 0.340816 M5 -0.147230848861288 3.720467 -0.0396 0.968551 0.484276 M6 14.0241977225673 3.720467 3.7695 0.000348 0.000174 M7 -18.6472308488613 3.720467 -5.0121 4e-06 2e-06 M8 -17.3043737060041 3.720467 -4.6511 1.6e-05 8e-06 M9 5.91666666666667 3.859298 1.5331 0.129961 0.064981 M10 6.65 3.859298 1.7231 0.089481 0.044741 M11 2.58333333333333 3.859298 0.6694 0.505554 0.252777 Multiple Linear Regression - Regression Statistics Multiple R 0.875078894705212 R-squared 0.765763071958496 Adjusted R-squared 0.723810189324197 F-TEST (value) 18.2529309996076 F-TEST (DF numerator) 12 F-TEST (DF denominator) 67 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.68450099095196 Sum Squared Residuals 2993.73108436853 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 94.5451863354039 12.1548136645961 2 110.2 97.7451863354037 12.4548136645963 3 125.9 112.312629399586 13.5873706004141 4 100.1 98.5697722567288 1.53022774327122 5 106.4 99.955486542443 6.44451345755693 6 114.8 114.126915113872 0.67308488612836 7 81.3 81.455486542443 -0.155486542443061 8 87 82.7983436853002 4.20165631469979 9 104.2 106.019384057971 -1.819384057971 10 108 106.752717391304 1.24728260869565 11 105 102.686050724638 2.31394927536232 12 94.5 100.102717391304 -5.60271739130435 13 92 94.5451863354037 -2.5451863354037 14 95.9 97.7451863354037 -1.84518633540372 15 108.8 112.312629399586 -3.51262939958592 16 103.4 98.5697722567288 4.83022774327123 17 102.1 99.955486542443 2.14451345755693 18 110.1 114.126915113872 -4.02691511387164 19 83.2 81.455486542443 1.74451345755694 20 82.7 82.7983436853002 -0.0983436853002035 21 106.8 106.019384057971 0.78061594202898 22 113.7 106.752717391304 6.94728260869566 23 102.5 102.686050724638 -0.186050724637679 24 96.6 100.102717391304 -3.50271739130435 25 92.1 94.5451863354037 -2.44518633540371 26 95.6 97.7451863354037 -2.14518633540373 27 102.3 112.312629399586 -10.0126293995859 28 98.6 98.5697722567288 0.0302277432712211 29 98.2 99.955486542443 -1.75548654244306 30 104.5 114.126915113872 -9.62691511387164 31 84 81.455486542443 2.54451345755694 32 73.8 82.7983436853002 -8.99834368530021 33 103.9 106.019384057971 -2.11938405797101 34 106 106.752717391304 -0.752717391304345 35 97.2 102.686050724638 -5.48605072463767 36 102.6 100.102717391304 2.49728260869565 37 89 94.5451863354037 -5.5451863354037 38 93.8 97.7451863354037 -3.94518633540373 39 116.7 122.540527950311 -5.84052795031056 40 106.8 108.797670807453 -1.99767080745342 41 98.5 110.183385093168 -11.6833850931677 42 118.7 124.354813664596 -5.65481366459628 43 90 91.6833850931677 -1.6833850931677 44 91.9 93.0262422360248 -1.12624223602484 45 113.3 116.247282608696 -2.94728260869566 46 113.1 116.980615942029 -3.88061594202899 47 104.1 112.913949275362 -8.81394927536232 48 108.7 110.330615942029 -1.63061594202899 49 96.7 104.773084886128 -8.07308488612834 50 101 107.973084886128 -6.97308488612837 51 116.9 122.540527950311 -5.64052795031056 52 105.8 108.797670807453 -2.99767080745342 53 99 110.183385093168 -11.1833850931677 54 129.4 124.354813664596 5.04518633540373 55 83 91.6833850931677 -8.6833850931677 56 88.9 93.0262422360248 -4.12624223602484 57 115.9 116.247282608696 -0.347282608695653 58 104.2 116.980615942029 -12.7806159420290 59 113.4 112.913949275362 0.486050724637686 60 112.2 110.330615942029 1.86938405797101 61 100.8 104.773084886128 -3.97308488612835 62 107.3 107.973084886128 -0.673084886128371 63 126.6 122.540527950311 4.05947204968943 64 102.9 108.797670807453 -5.89767080745341 65 117.9 110.183385093168 7.7166149068323 66 128.8 124.354813664596 4.44518633540374 67 87.5 91.6833850931677 -4.1833850931677 68 93.8 93.0262422360248 0.773757763975149 69 122.7 116.247282608696 6.45271739130434 70 126.2 116.980615942029 9.21938405797102 71 124.6 112.913949275362 11.6860507246377 72 116.7 110.330615942029 6.36938405797101 73 115.2 104.773084886128 10.4269151138717 74 111.1 107.973084886128 3.12691511387163 75 129.9 122.540527950311 7.35947204968944 76 113.3 108.797670807453 4.50232919254658 77 118.5 110.183385093168 8.3166149068323 78 133.5 124.354813664596 9.14518633540373 79 102.1 91.6833850931677 10.4166149068323 80 102.4 93.0262422360249 9.37375776397515

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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