JJ Workshop 7, Optimaliseren model (2)

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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: Fri, 20 Nov 2009 13:17:21 -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/Nov/20/t1258748444yn0pxswrilq5egg.htm/, Retrieved Fri, 20 Nov 2009 21:20:56 +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/Nov/20/t1258748444yn0pxswrilq5egg.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:

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Dataseries X:

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95.1 93.8 111.7 97 93.8 98.6 112.7 107.6 96.9 102.9 101 95.1 97.4 95.4 97 111.4 96.5 112.7 87.4 89.2 102.9 96.8 87.1 97.4 114.1 110.5 111.4 110.3 110.8 87.4 103.9 104.2 96.8 101.6 88.9 114.1 94.6 89.8 110.3 95.9 90 103.9 104.7 93.9 101.6 102.8 91.3 94.6 98.1 87.8 95.9 113.9 99.7 104.7 80.9 73.5 102.8 95.7 79.2 98.1 113.2 96.9 113.9 105.9 95.2 80.9 108.8 95.6 95.7 102.3 89.7 113.2 99 92.8 105.9 100.7 88 108.8 115.5 101.1 102.3 100.7 92.7 99 109.9 95.8 100.7 114.6 103.8 115.5 85.4 81.8 100.7 100.5 87.1 109.9 114.8 105.9 114.6 116.5 108.1 85.4 112.9 102.6 100.5 102 93.7 114.8 106 103.5 116.5 105.3 100.6 112.9 118.8 113.3 102 106.1 102.4 106 109.3 102.1 105.3 117.2 106.9 118.8 92.5 87.3 106.1 104.2 93.1 109.3 112.5 109.1 117.2 122.4 120.3 92.5 113.3 104.9 104.2 100 92.6 112.5 110.7 109.8 122.4 112.8 111.4 113.3 109.8 117.9 100 117.3 121.6 110.7 109.1 117.8 112.8 115.9 124.2 109.8 96 106.8 117.3 99.8 102.7 109.1 116.8 116.8 115.9 115.7 113.6 96 99.4 96.1 99 etc...

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TIA[t] = + 34.5997540927041 + 0.298221021904011IAidM[t] + 0.3378221767271`TIA(t-3)`[t] -1.02304293176696M1[t] + 2.56849582970055M2[t] + 11.8907715171465M3[t] + 6.85428025389231M4[t] + 5.83103077546227M5[t] + 10.3857785141985M6[t] -8.11533998012746M7[t] + 2.61781806550856M8[t] + 8.80566945224169M9[t] + 16.9982285968716M10[t] + 9.45582905532634M11[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) 34.5997540927041 11.151053 3.1028 0.003273 0.001636 IAidM 0.298221021904011 0.071117 4.1934 0.000124 6.2e-05 `TIA(t-3)` 0.3378221767271 0.122632 2.7548 0.008386 0.004193 M1 -1.02304293176696 2.310845 -0.4427 0.660048 0.330024 M2 2.56849582970055 2.522807 1.0181 0.313951 0.156975 M3 11.8907715171465 3.429961 3.4667 0.001153 0.000577 M4 6.85428025389231 3.162832 2.1671 0.035438 0.017719 M5 5.83103077546227 2.977952 1.9581 0.056303 0.028152 M6 10.3857785141985 2.584277 4.0188 0.000215 0.000107 M7 -8.11533998012746 2.404222 -3.3755 0.001506 0.000753 M8 2.61781806550856 2.50453 1.0452 0.301377 0.150688 M9 8.80566945224169 2.544644 3.4605 0.001174 0.000587 M10 16.9982285968716 4.754544 3.5752 0.000836 0.000418 M11 9.45582905532634 3.259021 2.9014 0.005682 0.002841 Multiple Linear Regression - Regression Statistics Multiple R 0.938876145706808 R-squared 0.881488416977271 Adjusted R-squared 0.847996013079543 F-TEST (value) 26.3190549017914 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.50877077042316 Sum Squared Residuals 566.327726691294 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 99.2845801559503 -4.18458015595026 2 97 98.450648402293 -1.45064840229292 3 112.7 111.314076491578 1.38592350842182 4 102.9 103.701246565649 -0.801246565648725 5 97.4 101.649821500338 -4.24982150033771 6 111.4 111.836420537784 -0.436420537783846 7 87.4 87.847631251633 -0.447631251633005 8 96.8 96.0965031792716 0.703496820728446 9 114.1 113.992236952738 0.107763047262040 10 110.3 114.166530162489 -3.86653016248863 11 103.9 107.831400337612 -3.93140033761166 12 101.6 99.6571133045328 1.94288669546721 13 94.6 97.6187450209164 -3.01874502091646 14 95.9 99.1078660557113 -3.20786605571133 15 104.7 108.816212722111 -4.1162127221106 16 102.8 100.639591564816 2.16040843518373 17 98.1 99.0117373394674 -0.911737339467426 18 113.9 110.08815039406 3.81184960594011 19 80.9 83.1317789900673 -2.23177899006733 20 95.7 93.9770326299388 1.72296737006117 21 113.2 110.780986496661 2.41901350333886 22 105.9 107.31843807206 -1.41843807205991 23 108.8 104.895095154837 3.90490484516264 24 102.3 99.5916501630016 2.70834983699839 25 99 97.0269905090292 1.97300949097075 26 100.7 100.166752677866 0.533247322133904 27 115.5 111.199879603528 4.30012039647155 28 100.7 102.543518573081 -1.84351857308113 29 109.9 103.019051962990 6.88094803701041 30 114.6 114.959336092519 -0.359336092519019 31 85.4 84.8975869007437 0.502413099256293 32 100.5 100.319280388360 0.180719611639698 33 114.8 113.701451217506 1.09854878249378 34 116.5 112.685689049894 3.8143109501064 35 112.9 108.604188756456 4.29581124354449 36 102 101.325049733381 0.67495026661899 37 106 103.798870516709 2.20112948329057 38 105.3 105.309408478438 -0.00940847843775233 39 118.8 114.736829417739 4.06317058226074 40 106.1 107.801017722640 -1.70101772263975 41 109.3 106.451826413930 2.84817358607048 42 117.2 116.998634443621 0.201365556379122 43 92.5 88.3620422755421 4.13795772445789 44 104.2 101.905913213748 2.29408678625189 45 112.5 115.534096147090 -3.03409614708951 46 122.4 118.722522971885 3.67747702811506 47 113.3 110.540039160725 2.75996083927499 48 100 100.220015602814 -0.220015602814265 49 110.7 107.670813797395 3.02918620260541 50 112.8 108.665324385692 4.13467561430809 51 109.8 115.433001765044 -5.63300176504351 52 117.3 115.114625573814 2.18537442618588 53 109.1 113.667562783276 -4.56756278327575 54 115.9 119.117458532016 -3.21745853201637 55 96 97.9609605820139 -1.96096058201385 56 99.8 104.701270588681 -4.9012705886812 57 116.8 117.391229186005 -0.59122918600517 58 115.7 117.906819743673 -2.20681974367292 59 99.4 106.429276590370 -7.02927659037046 60 94.3 99.4061711962703 -5.10617119627032 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.130010385281992 0.260020770563984 0.869989614718008 18 0.0662062631748249 0.132412526349650 0.933793736825175 19 0.0400664367385688 0.0801328734771377 0.959933563261431 20 0.0184216635902407 0.0368433271804813 0.98157833640976 21 0.0181739333780818 0.0363478667561637 0.981826066621918 22 0.0105814829498701 0.0211629658997401 0.98941851705013 23 0.0503261007822526 0.100652201564505 0.949673899217747 24 0.0292680309317347 0.0585360618634693 0.970731969068265 25 0.0207002341356536 0.0414004682713071 0.979299765864346 26 0.0578773995050915 0.115754799010183 0.942122600494908 27 0.118318201188694 0.236636402377388 0.881681798811306 28 0.089760434685679 0.179520869371358 0.910239565314321 29 0.327538363598708 0.655076727197417 0.672461636401292 30 0.244100112650181 0.488200225300363 0.755899887349819 31 0.184809646026605 0.369619292053211 0.815190353973394 32 0.126936678751184 0.253873357502369 0.873063321248816 33 0.085475766473833 0.170951532947666 0.914524233526167 34 0.0917775182832606 0.183555036566521 0.90822248171674 35 0.105934648733168 0.211869297466337 0.894065351266832 36 0.0767698889034632 0.153539777806926 0.923230111096537 37 0.0558966312672782 0.111793262534556 0.944103368732722 38 0.0396151226737504 0.0792302453475009 0.96038487732625 39 0.06598040566108 0.13196081132216 0.93401959433892 40 0.0615639655985189 0.123127931197038 0.938436034401481 41 0.0439470406739921 0.0878940813479842 0.956052959326008 42 0.0385600347253864 0.0771200694507729 0.961439965274614 43 0.043352462416866 0.086704924833732 0.956647537583134 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 4 0.148148148148148 NOK 10% type I error level 10 0.370370370370370 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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