Model 5

*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: Sun, 20 Dec 2009 04:37:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/20/t1261309117wl644xjss9jlob6.htm/, Retrieved Sun, 20 Dec 2009 12:38:49 +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/2009/Dec/20/t1261309117wl644xjss9jlob6.htm/}, year = {2009}, } @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 = {2009}, 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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95,3 100,0 100,6 90,7 95,3 114,2 88,4 90,7 91,5 86,0 88,4 94,7 86,0 86,0 110,6 95,3 86,0 71,3 95,3 95,3 104,1 88,4 95,3 112,3 86,0 88,4 110,2 81,4 86,0 112,9 83,7 81,4 95,1 95,3 83,7 103,1 88,4 95,3 101,9 86,0 88,4 100,4 83,7 86,0 106,9 76,7 83,7 100,7 79,1 76,7 114,3 86,0 79,1 73,3 86,0 86,0 105,9 79,1 86,0 113,9 76,7 79,1 112,1 69,8 76,7 117,5 69,8 69,8 97,5 76,7 69,8 112,3 69,8 76,7 106,9 67,4 69,8 120,9 65,1 67,4 92,7 58,1 65,1 110,9 60,5 58,1 116,5 65,1 60,5 77,1 62,8 65,1 113,1 55,8 62,8 115,9 51,2 55,8 123,5 48,8 51,2 123,6 48,8 48,8 101,5 53,5 48,8 121,0 48,8 53,5 112,2 46,5 48,8 126,0 44,2 46,5 101,8 39,5 44,2 117,9 41,9 39,5 122,2 48,8 41,9 82,7 46,5 48,8 120,5 41,9 46,5 120,3 39,5 41,9 134,2 37,2 39,5 128,2 37,2 37,2 100,5 41,9 37,2 126,0 39,5 41,9 122,9 39,5 39,5 106,1 34,9 39,5 130,4 34,9 34,9 121,3 34,9 34,9 126,1 41,9 34,9 88,7 41,9 41,9 118,7 39,5 41,9 129,3 39,5 39,5 136,2 41,9 39,5 123,0 46,5 41,9 103,5

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkloosheid(Y(t))[t] = + 11.5841647429370 + 1.04632041693899`Y(t-1)`[t] -0.0950668208423679Productie[t] -12.7609495083958M1[t] -9.424817754117M2[t] -10.6989575038838M3[t] -11.7292539613326M4[t] -5.15362859834418M5[t] -3.57859488699885M6[t] -8.66323485599034M7[t] -12.8218646585940M8[t] -9.01873321102618M9[t] -9.638801525644M10[t] -7.52752597007651M11[t] + 0.120237492740617t + 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) 11.5841647429370 8.681423 1.3344 0.18895 0.094475 `Y(t-1)` 1.04632041693899 0.059428 17.6066 0 0 Productie -0.0950668208423679 0.052115 -1.8242 0.07492 0.03746 M1 -12.7609495083958 1.440477 -8.8588 0 0 M2 -9.424817754117 1.377321 -6.8429 0 0 M3 -10.6989575038838 1.448091 -7.3883 0 0 M4 -11.7292539613326 1.389391 -8.442 0 0 M5 -5.15362859834418 1.36825 -3.7666 0.000488 0.000244 M6 -3.57859488699885 2.351778 -1.5217 0.13525 0.067625 M7 -8.66323485599034 1.451651 -5.9678 0 0 M8 -12.8218646585940 1.470832 -8.7174 0 0 M9 -9.01873321102618 1.439944 -6.2633 0 0 M10 -9.638801525644 1.395543 -6.9068 0 0 M11 -7.52752597007651 1.641068 -4.587 3.7e-05 1.9e-05 t 0.120237492740617 0.070396 1.708 0.09468 0.04734 Multiple Linear Regression - Regression Statistics Multiple R 0.996305173007122 R-squared 0.992623997760752 Adjusted R-squared 0.990277087957355 F-TEST (value) 422.949359333691 F-TEST (DF numerator) 14 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.02453928565169 Sum Squared Residuals 180.34541004247 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.3 94.011772244439 1.28822775556099 2 90.7 91.2575267683888 -0.557526768388819 3 88.4 87.4485674265651 0.951432573434919 4 86 83.8277576762016 2.17224232379843 5 86 86.5008890798834 -0.500889079883405 6 95.3 91.9322863430744 3.36771365692559 7 95.3 93.5804720207265 1.71952797927350 8 88.4 88.762531779956 -0.362531779956076 9 86 85.6659301671544 0.334069832845593 10 81.4 82.3982499283492 -0.99824992834923 11 83.7 81.5088784697321 2.19112153026787 12 95.3 90.80264432477 4.49735567523001 13 88.4 90.413329330618 -2.01332933061796 14 86 86.7926879320219 -0.792687932021884 15 83.7 82.5096823388668 1.19031766113325 16 76.7 79.7825007044215 -3.08250070442148 17 79.1 77.8612118781214 1.23878812187858 18 86 85.965391737398 0.0346082626019769 19 86 85.121421778565 0.878578221434994 20 79.1 80.322494901963 -1.22249490196307 21 76.7 77.1973732429087 -0.497373242908667 22 69.8 73.6730125878291 -3.87301258782912 23 69.8 70.5862511761055 -0.786251176105529 24 76.7 76.8270256904556 -0.127025690455605 25 69.8 71.9192853842283 -2.11928538422827 26 67.4 66.8251082625755 0.574891737424533 27 65.1 65.8409213526505 -0.740921352650539 28 58.1 60.7941092896515 -2.69410928965147 29 60.5 59.6333550300904 0.866644969909643 30 65.1 67.5854279760192 -2.48542797601918 31 62.8 64.0116938673624 -1.21169386736242 32 55.8 57.3005775001811 -1.50057750018111 33 51.2 53.1771956835146 -1.97719568351456 34 48.8 47.8547842616338 0.945215738366216 35 48.8 49.6761050499046 -0.876105049904624 36 53.5 55.4700655062956 -1.97006550629557 37 48.8 48.5836474736665 0.216352526333491 38 46.5 45.8103886334480 0.689611366552034 39 44.2 44.5505664818474 -0.350566481847442 40 39.5 39.7033947426174 -0.203394742617378 41 41.9 41.072764309111 0.827235690888995 42 48.8 49.0343439371241 -0.234343937124065 43 46.5 47.6960265099107 -1.19602650991073 44 41.9 41.2701106052565 0.629889394743483 45 39.5 39.0589768179366 0.441023182063362 46 37.2 36.6183779204601 0.581622079539923 47 37.2 39.0767049471421 -1.87670494714208 48 41.9 44.3002644784788 -2.40026447847883 49 39.5 36.8719655670482 2.62803443295175 50 39.5 39.4142884035659 0.0857115964341367 51 34.9 35.9502624000702 -1.05026240007018 52 34.9 31.0922375871081 3.8077624128919 53 34.9 37.3317797027938 -2.43177970279381 54 41.9 42.5825500063843 -0.682550006384315 55 41.9 42.0903858234353 -0.190385823435347 56 39.5 37.0442852126432 2.45571478735676 57 39.5 37.8005240884857 1.69947591151427 58 41.9 38.5555753017278 3.34442469827221 59 46.5 45.1520603571156 1.34793964288436 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.661345794156611 0.677308411686777 0.338654205843389 19 0.607522648886354 0.784954702227292 0.392477351113646 20 0.477272636688031 0.954545273376062 0.522727363311969 21 0.357684124951082 0.715368249902165 0.642315875048918 22 0.461584622014903 0.923169244029806 0.538415377985097 23 0.477383599257358 0.954767198514715 0.522616400742642 24 0.600799974313914 0.798400051372172 0.399200025686086 25 0.560763658117177 0.878472683765647 0.439236341882823 26 0.622426126324596 0.755147747350808 0.377573873675404 27 0.545277453458666 0.909445093082668 0.454722546541334 28 0.596932135865741 0.806135728268518 0.403067864134259 29 0.646357906218245 0.707284187563511 0.353642093781755 30 0.668782315122546 0.662435369754909 0.331217684877454 31 0.600480983078841 0.799038033842318 0.399519016921159 32 0.548824705030216 0.902350589939569 0.451175294969784 33 0.53988859933738 0.92022280132524 0.46011140066262 34 0.585872211256788 0.828255577486424 0.414127788743212 35 0.487983358822985 0.97596671764597 0.512016641177015 36 0.468632618205479 0.937265236410958 0.531367381794521 37 0.474729593360066 0.949459186720132 0.525270406639934 38 0.42859676450598 0.85719352901196 0.57140323549402 39 0.299814724165912 0.599629448331824 0.700185275834088 40 0.524308161756691 0.951383676486617 0.475691838243309 41 0.943853704802321 0.112292590395358 0.056146295197679 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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