paper_multipleregression_2dummies

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

Title produced by software: Multiple Regression

Date of computation: Wed, 09 Jan 2008 06:25:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/09/t1199885093g8afn5ybttuxngs.htm/, Retrieved Wed, 09 Jan 2008 14:25:03 +0100

User-defined keywords:

s0650921, s0650125

Dataseries X:

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102.7 0 0 103.2 0 0 105.6 0 0 103.9 0 0 107.2 0 0 100.7 0 0 92.1 0 0 90.3 0 0 93.4 0 0 98.5 0 0 100.8 0 0 102.3 0 0 104.7 0 0 101.1 0 0 101.4 0 0 99.5 0 0 98.4 0 0 96.3 0 0 100.7 0 0 101.2 0 0 100.3 0 0 97.8 0 0 97.4 0 0 98.6 0 0 99.7 0 0 99.0 0 0 98.1 0 0 97.0 0 0 98.5 0 0 103.8 0 0 114.4 0 0 124.5 0 0 134.2 0 0 131.8 0 0 125.6 0 0 119.9 0 0 114.9 0 0 115.5 0 0 112.5 0 0 111.4 0 0 115.3 0 0 110.8 0 0 103.7 0 0 111.1 0 1 113.0 0 1 111.2 0 1 117.6 0 1 121.7 0 1 127.3 0 1 129.8 0 1 137.1 0 1 141.4 0 1 137.4 0 1 130.7 0 1 117.2 0 1 110.8 0 -1 111.4 0 -1 108.2 0 -1 108.8 0 -1 110.2 0 -1 109.5 0 -1 109.5 0 -1 116.0 0 -1 111.2 0 -1 112.1 0 -1 114.0 0 -1 119.1 0 -1 114.1 1 -1 115.1 1 -1 115.4 1 -1 110.8 1 0 116.0 1 0 119.2 1 0 126.5 1 0 127.8 1 0 131.3 1 0 140.3 1 0 137.3 1 0 143.0 1 0 134.5 1 0 139.9 1 0 159.3 1 0 170.4 1 0 175.0 1 0 175.8 1 0 180.9 1 0 180.3 1 0 169.6 1 0 172.3 1 0 184.8 1 0 177.7 1 0 184.6 1 0 211.4 1 0 215.3 1 0 215.9 1 0

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation prijsindex[t] = + 109.925373134328 + 46.3420967451897ontkoppelde_bedrijfstoeslag[t] + 10.329718875502oogstomvang[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) 109.925373134328 2.389091 46.0114 0 0 ontkoppelde_bedrijfstoeslag 46.3420967451897 4.419293 10.4863 0 0 oogstomvang 10.329718875502 3.786072 2.7283 0.007625 0.003812 Multiple Linear Regression - Regression Statistics Multiple R 0.7425997210836 R-squared 0.55145434575344 Adjusted R-squared 0.541703353269819 F-TEST (value) 56.5536632993759 F-TEST (DF numerator) 2 F-TEST (DF denominator) 92 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19.5555528610616 Sum Squared Residuals 35182.6075885632 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.7 109.925373134329 -7.22537313432858 2 103.2 109.925373134328 -6.72537313432836 3 105.6 109.925373134328 -4.3253731343283 4 103.9 109.925373134328 -6.02537313432835 5 107.2 109.925373134328 -2.72537313432835 6 100.7 109.925373134328 -9.22537313432835 7 92.1 109.925373134328 -17.8253731343284 8 90.3 109.925373134328 -19.6253731343284 9 93.4 109.925373134328 -16.5253731343284 10 98.5 109.925373134328 -11.4253731343284 11 100.8 109.925373134328 -9.12537313432836 12 102.3 109.925373134328 -7.62537313432836 13 104.7 109.925373134328 -5.22537313432836 14 101.1 109.925373134328 -8.82537313432836 15 101.4 109.925373134328 -8.52537313432835 16 99.5 109.925373134328 -10.4253731343284 17 98.4 109.925373134328 -11.5253731343284 18 96.3 109.925373134328 -13.6253731343284 19 100.7 109.925373134328 -9.22537313432835 20 101.2 109.925373134328 -8.72537313432836 21 100.3 109.925373134328 -9.62537313432836 22 97.8 109.925373134328 -12.1253731343284 23 97.4 109.925373134328 -12.5253731343284 24 98.6 109.925373134328 -11.3253731343284 25 99.7 109.925373134328 -10.2253731343284 26 99 109.925373134328 -10.9253731343284 27 98.1 109.925373134328 -11.8253731343284 28 97 109.925373134328 -12.9253731343284 29 98.5 109.925373134328 -11.4253731343284 30 103.8 109.925373134328 -6.12537313432836 31 114.4 109.925373134328 4.47462686567165 32 124.5 109.925373134328 14.5746268656716 33 134.2 109.925373134328 24.2746268656716 34 131.8 109.925373134328 21.8746268656717 35 125.6 109.925373134328 15.6746268656716 36 119.9 109.925373134328 9.97462686567165 37 114.9 109.925373134328 4.97462686567165 38 115.5 109.925373134328 5.57462686567164 39 112.5 109.925373134328 2.57462686567164 40 111.4 109.925373134328 1.47462686567165 41 115.3 109.925373134328 5.37462686567164 42 110.8 109.925373134328 0.87462686567164 43 103.7 109.925373134328 -6.22537313432836 44 111.1 120.255092009830 -9.15509200983037 45 113 120.255092009830 -7.25509200983037 46 111.2 120.255092009830 -9.05509200983037 47 117.6 120.255092009830 -2.65509200983037 48 121.7 120.255092009830 1.44490799016963 49 127.3 120.255092009830 7.04490799016963 50 129.8 120.255092009830 9.54490799016964 51 137.1 120.255092009830 16.8449079901696 52 141.4 120.255092009830 21.1449079901696 53 137.4 120.255092009830 17.1449079901696 54 130.7 120.255092009830 10.4449079901696 55 117.2 120.255092009830 -3.05509200983037 56 110.8 99.5956542588263 11.2043457411737 57 111.4 99.5956542588263 11.8043457411737 58 108.2 99.5956542588263 8.60434574117366 59 108.8 99.5956542588263 9.20434574117365 60 110.2 99.5956542588263 10.6043457411737 61 109.5 99.5956542588263 9.90434574117365 62 109.5 99.5956542588263 9.90434574117365 63 116 99.5956542588264 16.4043457411736 64 111.2 99.5956542588263 11.6043457411737 65 112.1 99.5956542588263 12.5043457411736 66 114 99.5956542588263 14.4043457411737 67 119.1 99.5956542588264 19.5043457411736 68 114.1 145.937751004016 -31.8377510040161 69 115.1 145.937751004016 -30.8377510040161 70 115.4 145.937751004016 -30.5377510040161 71 110.8 156.267469879518 -45.4674698795181 72 116 156.267469879518 -40.2674698795181 73 119.2 156.267469879518 -37.0674698795181 74 126.5 156.267469879518 -29.7674698795181 75 127.8 156.267469879518 -28.4674698795181 76 131.3 156.267469879518 -24.9674698795181 77 140.3 156.267469879518 -15.9674698795181 78 137.3 156.267469879518 -18.9674698795181 79 143 156.267469879518 -13.2674698795181 80 134.5 156.267469879518 -21.7674698795181 81 139.9 156.267469879518 -16.3674698795181 82 159.3 156.267469879518 3.03253012048194 83 170.4 156.267469879518 14.1325301204819 84 175 156.267469879518 18.7325301204819 85 175.8 156.267469879518 19.5325301204819 86 180.9 156.267469879518 24.6325301204819 87 180.3 156.267469879518 24.0325301204819 88 169.6 156.267469879518 13.3325301204819 89 172.3 156.267469879518 16.0325301204819 90 184.8 156.267469879518 28.5325301204819 91 177.7 156.267469879518 21.4325301204819 92 184.6 156.267469879518 28.3325301204819 93 211.4 156.267469879518 55.132530120482 94 215.3 156.267469879518 59.032530120482 95 215.9 156.267469879518 59.6325301204819

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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