paper: multiple regression: samenwerking

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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: Tue, 16 Dec 2008 13:44:10 -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/Dec/16/t1229460282wg87r7k2gedq24d.htm/, Retrieved Tue, 16 Dec 2008 21:44:43 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t1229460282wg87r7k2gedq24d.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

paper: multiple regression: samenwerking

Dataseries X:

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25 0 23.6 0 22.3 0 21.8 0 20.8 0 19.7 0 18.3 0 17.4 0 17 0 18.1 0 23.9 0 25.6 0 25.3 0 23.6 0 21.9 0 21.4 0 20.6 0 20.5 0 20.2 0 20.6 0 19.7 0 19.3 0 22.8 0 23.5 0 23.8 0 22.6 0 22 0 21.7 0 20.7 0 20.2 0 19.1 0 19.5 0 18.7 0 18.6 0 22.2 0 23.2 0 23.5 1 21.3 1 20 1 18.7 1 18.9 1 18.3 1 18.4 1 19.9 1 19.2 1 18.5 1 20.9 1 20.5 1 19.4 1 18.1 1 17 1 17 1 17.3 1 16.7 1 15.5 1 15.3 1 13.7 1 14.1 1 17.3 1 18.1 1

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 computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Werklozen[t] = + 24.7555555555556 -1.31388888888889Samenwerking[t] + 0.593611111111107M1[t] -0.909444444444443M2[t] -2.0525M3[t] -2.51555555555556M4[t] -2.91861111111111M5[t] -3.44166666666667M6[t] -4.16472222222222M7[t] -3.86777777777778M8[t] -4.69083333333333M9[t] -4.57388888888889M10[t] -0.816944444444445M11[t] -0.0569444444444444t + 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) 24.7555555555556 0.808906 30.6038 0 0 Samenwerking -1.31388888888889 0.726419 -1.8087 0.077033 0.038517 M1 0.593611111111107 0.901706 0.6583 0.513614 0.256807 M2 -0.909444444444443 0.896571 -1.0144 0.315718 0.157859 M3 -2.0525 0.891899 -2.3013 0.025958 0.012979 M4 -2.51555555555556 0.887699 -2.8338 0.006809 0.003404 M5 -2.91861111111111 0.883976 -3.3017 0.001864 0.000932 M6 -3.44166666666667 0.880736 -3.9077 0.000304 0.000152 M7 -4.16472222222222 0.877986 -4.7435 2.1e-05 1e-05 M8 -3.86777777777778 0.875729 -4.4166 6e-05 3e-05 M9 -4.69083333333333 0.87397 -5.3673 3e-06 1e-06 M10 -4.57388888888889 0.872711 -5.241 4e-06 2e-06 M11 -0.816944444444445 0.871955 -0.9369 0.353697 0.176849 t -0.0569444444444444 0.02097 -2.7155 0.009289 0.004644 Multiple Linear Regression - Regression Statistics Multiple R 0.891763263359902 R-squared 0.795241717878302 Adjusted R-squared 0.737375246843909 F-TEST (value) 13.7427028754812 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 9.53037648798727e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.37828308094082 Sum Squared Residuals 87.3845555555556 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 25.2922222222222 -0.292222222222238 2 23.6 23.7322222222222 -0.13222222222222 3 22.3 22.5322222222222 -0.232222222222220 4 21.8 22.0122222222222 -0.212222222222220 5 20.8 21.5522222222222 -0.75222222222222 6 19.7 20.9722222222222 -1.27222222222222 7 18.3 20.1922222222222 -1.89222222222222 8 17.4 20.4322222222222 -3.03222222222222 9 17 19.5522222222222 -2.55222222222222 10 18.1 19.6122222222222 -1.51222222222222 11 23.9 23.3122222222222 0.587777777777779 12 25.6 24.0722222222222 1.52777777777778 13 25.3 24.6088888888889 0.691111111111117 14 23.6 23.0488888888889 0.551111111111112 15 21.9 21.8488888888889 0.0511111111111101 16 21.4 21.3288888888889 0.07111111111111 17 20.6 20.8688888888889 -0.268888888888888 18 20.5 20.2888888888889 0.211111111111112 19 20.2 19.5088888888889 0.69111111111111 20 20.6 19.7488888888889 0.851111111111113 21 19.7 18.8688888888889 0.831111111111112 22 19.3 18.9288888888889 0.371111111111111 23 22.8 22.6288888888889 0.171111111111112 24 23.5 23.3888888888889 0.111111111111112 25 23.8 23.9255555555556 -0.125555555555551 26 22.6 22.3655555555556 0.234444444444444 27 22 21.1655555555556 0.834444444444445 28 21.7 20.6455555555556 1.05444444444444 29 20.7 20.1855555555556 0.514444444444443 30 20.2 19.6055555555556 0.594444444444444 31 19.1 18.8255555555556 0.274444444444445 32 19.5 19.0655555555556 0.434444444444443 33 18.7 18.1855555555556 0.514444444444443 34 18.6 18.2455555555556 0.354444444444444 35 22.2 21.9455555555556 0.254444444444443 36 23.2 22.7055555555556 0.494444444444443 37 23.5 21.9283333333333 1.57166666666667 38 21.3 20.3683333333333 0.931666666666666 39 20 19.1683333333333 0.831666666666667 40 18.7 18.6483333333333 0.0516666666666663 41 18.9 18.1883333333333 0.711666666666665 42 18.3 17.6083333333333 0.691666666666668 43 18.4 16.8283333333333 1.57166666666667 44 19.9 17.0683333333333 2.83166666666667 45 19.2 16.1883333333333 3.01166666666667 46 18.5 16.2483333333333 2.25166666666667 47 20.9 19.9483333333333 0.951666666666666 48 20.5 20.7083333333333 -0.208333333333334 49 19.4 21.245 -1.84500000000000 50 18.1 19.685 -1.585 51 17 18.485 -1.485 52 17 17.965 -0.965 53 17.3 17.505 -0.205 54 16.7 16.925 -0.225000000000001 55 15.5 16.145 -0.644999999999999 56 15.3 16.385 -1.085 57 13.7 15.505 -1.805 58 14.1 15.565 -1.465 59 17.3 19.265 -1.965 60 18.1 20.025 -1.925 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0190324329328568 0.0380648658657135 0.980967567067143 18 0.0346430540191285 0.069286108038257 0.965356945980872 19 0.179736783015320 0.359473566030641 0.82026321698468 20 0.588510069531831 0.822979860936338 0.411489930468169 21 0.693532345476161 0.612935309047678 0.306467654523839 22 0.696993557451901 0.606012885096197 0.303006442548099 23 0.825491137058008 0.349017725883984 0.174508862941992 24 0.956835021580941 0.0863299568381171 0.0431649784190586 25 0.963279480092617 0.0734410398147652 0.0367205199073826 26 0.950311397478002 0.099377205043996 0.049688602521998 27 0.926070609479173 0.147858781041654 0.073929390520827 28 0.91104074718589 0.17791850562822 0.08895925281411 29 0.862202117115267 0.275595765769466 0.137797882884733 30 0.797861601694174 0.404276796611653 0.202138398305826 31 0.728686788426443 0.542626423147114 0.271313211573557 32 0.677524129196399 0.644951741607202 0.322475870803601 33 0.607875385921405 0.78424922815719 0.392124614078595 34 0.556073704814094 0.887852590371811 0.443926295185905 35 0.508375039800467 0.983249920399066 0.491624960199533 36 0.445584632529034 0.891169265058068 0.554415367470966 37 0.37108127583042 0.74216255166084 0.62891872416958 38 0.275413381116461 0.550826762232921 0.72458661888354 39 0.189018194838614 0.378036389677227 0.810981805161386 40 0.192760862249283 0.385521724498566 0.807239137750717 41 0.220666696731568 0.441333393463136 0.779333303268432 42 0.349524148210897 0.699048296421795 0.650475851789103 43 0.307298980305354 0.614597960610708 0.692701019694646 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 1 0.037037037037037 OK 10% type I error level 5 0.185185185185185 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test 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)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$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') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$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() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() 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') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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