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Q3 - metaalverwerking - linear trend

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 08:55:58 -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/18/t1195401036hrvxmw2t6wubonl.htm/, Retrieved Sun, 18 Nov 2007 16:50:46 +0100

User-defined keywords:

Dataseries X:

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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 0 106.8 0 98.5 0 118.7 0 90 0 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 75.261054945055 -1.58593406593407x[t] + 26.9829413919414M1[t] + 26.6538388278388M2[t] + 21.9247362637363M3[t] + 20.4756336996337M4[t] + 11.4265311355311M5[t] + 13.9774285714286M6[t] + 30.248326007326M7[t] + 16.7992234432234M8[t] + 17.2901208791209M9[t] + 33.4010183150183M10[t] -0.708084249084255M11[t] + 0.449102564102564t + 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) 75.261054945055 2.703851 27.8348 0 0 x -1.58593406593407 2.640786 -0.6006 0.551085 0.275542 M1 26.9829413919414 3.285369 8.2131 0 0 M2 26.6538388278388 3.277621 8.1321 0 0 M3 21.9247362637363 3.271582 6.7016 0 0 M4 20.4756336996337 3.267262 6.2669 0 0 M5 11.4265311355311 3.264667 3.5001 0.001045 0.000523 M6 13.9774285714286 3.263802 4.2826 9.3e-05 4.7e-05 M7 30.248326007326 3.264667 9.2654 0 0 M8 16.7992234432234 3.267262 5.1417 5e-06 3e-06 M9 17.2901208791209 3.271582 5.2849 3e-06 2e-06 M10 33.4010183150183 3.277621 10.1906 0 0 M11 -0.708084249084255 3.285369 -0.2155 0.83031 0.415155 t 0.449102564102564 0.075167 5.9748 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.936067032778345 R-squared 0.876221489854456 Adjusted R-squared 0.841240606552454 F-TEST (value) 25.0485810289507 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.14219103293595 Sum Squared Residuals 1216.33791648352 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.8 102.693098901099 4.10690109890118 2 113.7 102.813098901099 10.8869010989011 3 102.5 98.533098901099 3.96690109890108 4 96.6 97.533098901099 -0.93309890109893 5 92.1 88.933098901099 3.16690109890104 6 95.6 91.9330989010989 3.66690109890109 7 102.3 108.653098901099 -6.35309890109889 8 98.6 95.653098901099 2.94690109890108 9 98.2 96.5930989010989 1.60690109890112 10 104.5 113.153098901099 -8.6530989010989 11 84 79.4930989010989 4.50690109890112 12 73.8 80.6502857142857 -6.8502857142857 13 103.9 108.082329670330 -4.18232967032969 14 106 108.202329670330 -2.20232967032967 15 97.2 103.922329670330 -6.72232967032967 16 102.6 102.922329670330 -0.32232967032967 17 89 94.3223296703297 -5.32232967032966 18 93.8 97.3223296703297 -3.52232967032967 19 116.7 114.042329670330 2.65767032967033 20 106.8 101.042329670330 5.75767032967034 21 98.5 101.982329670330 -3.48232967032968 22 118.7 118.542329670330 0.15767032967033 23 90 84.8823296703297 5.11767032967033 24 91.9 84.4535824175824 7.44641758241758 25 113.3 111.885626373626 1.41437362637360 26 113.1 112.005626373626 1.09437362637363 27 104.1 107.725626373626 -3.62562637362637 28 108.7 106.725626373626 1.97437362637364 29 96.7 98.1256263736263 -1.42562637362635 30 101 101.125626373626 -0.125626373626363 31 116.9 117.845626373626 -0.945626373626368 32 105.8 104.845626373626 0.954373626373634 33 99 105.785626373626 -6.78562637362638 34 129.4 122.345626373626 7.05437362637362 35 83 88.6856263736264 -5.68562637362638 36 88.9 89.8428131868132 -0.942813186813188 37 115.9 117.274857142857 -1.37485714285716 38 104.2 117.394857142857 -13.1948571428571 39 113.4 113.114857142857 0.285142857142869 40 112.2 112.114857142857 0.085142857142868 41 100.8 103.514857142857 -2.71485714285713 42 107.3 106.514857142857 0.785142857142858 43 126.6 123.234857142857 3.36514285714284 44 102.9 110.234857142857 -7.33485714285713 45 117.9 111.174857142857 6.72514285714285 46 128.8 127.734857142857 1.06514285714286 47 87.5 94.0748571428572 -6.57485714285715 48 93.8 95.232043956044 -1.43204395604396 49 122.7 122.664087912088 0.0359120879120657 50 126.2 122.784087912088 3.41591208791209 51 124.6 118.504087912088 6.09591208791208 52 116.7 117.504087912088 -0.804087912087903 53 115.2 108.904087912088 6.2959120879121 54 111.1 111.904087912088 -0.804087912087916 55 129.9 128.624087912088 1.27591208791208 56 113.3 115.624087912088 -2.32408791208791 57 118.5 116.564087912088 1.93591208791208 58 133.5 133.124087912088 0.375912087912074 59 102.1 99.464087912088 2.63591208791208 60 102.4 100.621274725275 1.77872527472527

Charts produced by software:

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Parameters:

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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