Multiple Lineair Regression 4

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 12 Dec 2008 08:05:09 -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/12/t1229094415b5fzv5fdu2yne25.htm/, Retrieved Fri, 12 Dec 2008 16:07:04 +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/12/t1229094415b5fzv5fdu2yne25.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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91.2 0 99.2 0 108.2 0 101.5 0 106.9 0 104.4 0 77.9 0 60 0 99.5 0 95 0 105.6 0 102.5 0 93.3 0 97.3 0 127 0 111.7 0 96.4 0 133 0 72.2 0 95.8 0 124.1 0 127.6 0 110.7 0 104.6 0 112.7 0 115.3 0 139.4 0 119 0 97.4 0 154 0 81.5 0 88.8 0 127.7 1 105.1 1 114.9 1 106.4 1 104.5 1 121.6 1 141.4 1 99 1 126.7 1 134.1 1 81.3 1 88.6 1 132.7 1 132.9 1 134.4 1 103.7 1 119.7 1 115 1 132.9 1 108.5 1 113.9 1 142 1 97.7 1 92.2 1 128.8 1 134.9 1 128.2 1 114.8 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Transportmiddelen[t] = + 86.8583333333334 -10.0888888888889Conjunctuur[t] + 3.68291666666671M1[t] + 8.37194444444446M2[t] + 27.7609722222222M3[t] + 5.21000000000002M4[t] + 4.81902777777777M5[t] + 29.3480555555555M6[t] -22.7429166666667M7[t] -20.4938888888889M8[t] + 18.2929166666667M9[t] + 14.1219444444444M10[t] + 13.0709722222222M11[t] + 0.710972222222222t + 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) 86.8583333333334 5.016644 17.314 0 0 Conjunctuur -10.0888888888889 4.827268 -2.09 0.042176 0.021088 M1 3.68291666666671 5.85441 0.6291 0.532406 0.266203 M2 8.37194444444446 5.839465 1.4337 0.158425 0.079213 M3 27.7609722222222 5.827814 4.7635 1.9e-05 1e-05 M4 5.21000000000002 5.819478 0.8953 0.375304 0.187652 M5 4.81902777777777 5.81447 0.8288 0.411498 0.205749 M6 29.3480555555555 5.8128 5.0489 7e-06 4e-06 M7 -22.7429166666667 5.81447 -3.9114 3e-04 0.00015 M8 -20.4938888888889 5.819478 -3.5216 0.000981 0.00049 M9 18.2929166666667 5.807787 3.1497 0.00287 0.001435 M10 14.1219444444444 5.799422 2.4351 0.018826 0.009413 M11 13.0709722222222 5.794397 2.2558 0.028882 0.014441 t 0.710972222222222 0.139351 5.102 6e-06 3e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.905358234767946 R-squared 0.81967353326213 Adjusted R-squared 0.768711705705776 F-TEST (value) 16.0840686562059 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 6.00297589414822e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.15909687444977 Sum Squared Residuals 3858.89655555555 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 91.2 91.252222222222 -0.0522222222220999 2 99.2 96.6522222222222 2.54777777777779 3 108.2 116.752222222222 -8.55222222222225 4 101.5 94.9122222222222 6.58777777777777 5 106.9 95.2322222222222 11.6677777777778 6 104.4 120.472222222222 -16.0722222222222 7 77.9 69.0922222222222 8.80777777777777 8 60 72.0522222222222 -12.0522222222222 9 99.5 111.55 -12.05 10 95 108.09 -13.0900000000000 11 105.6 107.75 -2.15000000000003 12 102.5 95.39 7.11 13 93.3 99.783888888889 -6.48388888888893 14 97.3 105.183888888889 -7.88388888888888 15 127 125.283888888889 1.71611111111111 16 111.7 103.443888888889 8.25611111111111 17 96.4 103.763888888889 -7.36388888888888 18 133 129.003888888889 3.99611111111112 19 72.2 77.6238888888889 -5.42388888888889 20 95.8 80.5838888888889 15.2161111111111 21 124.1 120.081666666667 4.01833333333333 22 127.6 116.621666666667 10.9783333333333 23 110.7 116.281666666667 -5.58166666666665 24 104.6 103.921666666667 0.67833333333333 25 112.7 108.315555555556 4.38444444444441 26 115.3 113.715555555556 1.58444444444443 27 139.4 133.815555555556 5.58444444444445 28 119 111.975555555556 7.02444444444445 29 97.4 112.295555555556 -14.8955555555555 30 154 137.535555555556 16.4644444444444 31 81.5 86.1555555555556 -4.65555555555556 32 88.8 89.1155555555556 -0.315555555555565 33 127.7 118.524444444444 9.17555555555556 34 105.1 115.064444444444 -9.96444444444445 35 114.9 114.724444444444 0.175555555555562 36 106.4 102.364444444444 4.03555555555556 37 104.5 106.758333333333 -2.25833333333337 38 121.6 112.158333333333 9.44166666666664 39 141.4 132.258333333333 9.14166666666667 40 99 110.418333333333 -11.4183333333333 41 126.7 110.738333333333 15.9616666666667 42 134.1 135.978333333333 -1.87833333333334 43 81.3 84.5983333333333 -3.29833333333334 44 88.6 87.5583333333333 1.04166666666665 45 132.7 127.056111111111 5.64388888888888 46 132.9 123.596111111111 9.3038888888889 47 134.4 123.256111111111 11.1438888888889 48 103.7 110.896111111111 -7.19611111111111 49 119.7 115.29 4.40999999999997 50 115 120.69 -5.69000000000001 51 132.9 140.79 -7.88999999999999 52 108.5 118.95 -10.45 53 113.9 119.27 -5.36999999999998 54 142 144.51 -2.50999999999999 55 97.7 93.13 4.57 56 92.2 96.09 -3.89 57 128.8 135.587777777778 -6.78777777777776 58 134.9 132.127777777778 2.77222222222224 59 128.2 131.787777777778 -3.58777777777778 60 114.8 119.427777777778 -4.62777777777778 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.680508043425299 0.638983913149402 0.319491956574701 18 0.842647592939526 0.314704814120949 0.157352407060475 19 0.81965041791647 0.360699164167061 0.180349582083530 20 0.937661781115012 0.124676437769975 0.0623382188849877 21 0.92057824827277 0.158843503454460 0.0794217517272302 22 0.930714052696621 0.138571894606758 0.0692859473033789 23 0.912216990628014 0.175566018743971 0.0877830093719856 24 0.876162965807752 0.247674068384496 0.123837034192248 25 0.814414741754679 0.371170516490642 0.185585258245321 26 0.738196096836585 0.523607806326831 0.261803903163415 27 0.652373243781227 0.695253512437546 0.347626756218773 28 0.660676701303609 0.678646597392783 0.339323298696391 29 0.83999372972819 0.320012540543620 0.160006270271810 30 0.910075026447186 0.179849947105629 0.0899249735528144 31 0.880707041970576 0.238585916058849 0.119292958029424 32 0.824867303045231 0.350265393909538 0.175132696954769 33 0.760800865216296 0.478398269567408 0.239199134783704 34 0.904418759482146 0.191162481035709 0.0955812405178543 35 0.904780838294316 0.190438323411368 0.095219161705684 36 0.847245609354648 0.305508781290704 0.152754390645352 37 0.850828390187238 0.298343219625523 0.149171609812762 38 0.811101799906963 0.377796400186074 0.188898200093037 39 0.790315638634204 0.419368722731591 0.209684361365796 40 0.77566883528255 0.448662329434901 0.224331164717451 41 0.864321533473015 0.271356933053969 0.135678466526985 42 0.766107220749974 0.467785558500052 0.233892779250026 43 0.818092047552222 0.363815904895556 0.181907952447778 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 0 0 OK 10% type I error level 0 0 OK

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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