Blog 3

*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: Tue, 14 Dec 2010 16:01:13 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342377jo2lbpyx7pxqayr.htm/, Retrieved Tue, 14 Dec 2010 16:59:47 +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/2010/Dec/14/t1292342377jo2lbpyx7pxqayr.htm/}, year = {2010}, } @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 = {2010}, 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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10 288.60 1.39 113.67 0.8764 8.1110 9 269.10 1.31 110.26 0.8399 7.9156 8 268.70 1.29 110.04 0.8236 7.9325 7 264.30 1.28 111.73 0.8357 8.0201 6 264.30 1.22 110.99 0.8277 7.9062 5 267.60 1.26 115.83 0.8571 7.8907 4 298.10 1.34 125.33 0.8746 7.9323 3 279.80 1.36 123.03 0.9016 8.0369 2 263.20 1.37 123.46 0.8760 8.0971 1 272.50 1.43 130.34 0.8831 8.1817 12 263.70 1.46 131.21 0.8997 8.4066 11 273.70 1.49 132.97 0.8989 8.4143 10 261.40 1.48 133.91 0.9156 8.3596 9 241.10 1.46 133.14 0.8914 8.5964 8 253.40 1.43 135.31 0.8627 8.6602 7 228.60 1.41 133.09 0.8609 8.9494 6 244.90 1.40 135.39 0.8567 8.9388 5 206.10 1.37 131.85 0.8844 8.7943 4 177.00 1.32 130.25 0.8976 8.7867 3 165.10 1.31 127.65 0.9197 8.8388 2 148.10 1.28 118.30 0.8869 8.7838 1 152.90 1.32 119.73 0.9182 9.2164 12 146.50 1.34 122.51 0.9045 9.4228 11 188.00 1.27 123.28 0.8306 8.8094 10 252.00 1.33 133.52 0.7867 8.5928 9 351.60 1.44 153.20 0.7992 8.1566 8 403.00 1.50 163.63 0.7928 7.9723 7 468.80 1.58 168.45 0.7931 8.0487 6 464.00 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Olie[t] = + 386.45427318052 + 0.56701815519588Maand[t] + 445.307733549336Dollar[t] + 0.254778211717494Yen[t] + 150.818766016759Pond[t] -108.357416744584Noorse_kroon[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) 386.45427318052 121.550312 3.1794 0.002487 0.001244 Maand 0.56701815519588 1.313911 0.4315 0.667853 0.333926 Dollar 445.307733549336 118.192058 3.7677 0.000422 0.000211 Yen 0.254778211717494 0.858014 0.2969 0.767696 0.383848 Pond 150.818766016759 178.96263 0.8427 0.403234 0.201617 Noorse_kroon -108.357416744584 15.845472 -6.8384 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.907506707840720 R-squared 0.823568424775901 Adjusted R-squared 0.806603850235122 F-TEST (value) 48.5463648260816 F-TEST (DF numerator) 5 F-TEST (DF denominator) 52 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 30.9175680466866 Sum Squared Residuals 49706.5927239179 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 288.6 293.353403013746 -4.75340301374643 2 269.1 271.961126744932 -2.86112674493149 3 268.7 258.142316483115 10.5576835168855 4 264.3 245.885593532205 18.4144064677949 5 264.3 229.546935126452 34.7530648735479 6 267.6 254.138964538376 13.4610354616239 7 298.1 289.748617947162 8.35138205283805 8 279.8 290.239685466972 -10.4396854669716 9 263.2 283.851222380255 -20.6512223802547 10 272.5 303.659318116762 -31.1593181167624 11 263.7 301.611415364613 -37.9114153646128 12 273.7 313.897031746773 -40.1970317467729 13 261.4 317.562251863507 -56.1622518635067 14 241.1 278.584049391579 -37.4840493915788 15 253.4 253.968966176344 -0.568966176344293 16 228.6 212.321747018785 16.278252981215 17 244.9 208.402791215268 36.4972087847318 18 206.1 213.409952722369 -7.30995272236906 19 177 192.984226829638 -15.9842268296384 20 165.1 184.989381305061 -19.8893813050612 21 148.1 169.693757259429 -21.5937572594292 22 152.9 145.148590181580 7.75140981841964 23 146.5 136.569040077785 9.9309599222154 24 188 160.347592419647 27.6524075803531 25 252 205.957239804139 46.0427601958606 26 351.6 308.538847305168 43.0611526948323 27 403 356.352661714665 46.6473382853351 28 468.8 384.405032214413 84.394967785587 29 464 380.330629316732 83.6693706832675 30 435.4 392.576613186401 42.8233868135986 31 382.2 390.517096005607 -8.31709600560731 32 360.6 371.354677544008 -10.7546775440078 33 329.5 334.463055029480 -4.96305502947965 34 320.2 332.602108062940 -12.4021080629395 35 315 325.629645610391 -10.6296456103911 36 322.7 334.077827006487 -11.3778270064866 37 289.7 337.520858928261 -47.8208589282614 38 270.3 306.649300356356 -36.3493003563565 39 247.8 275.353425939469 -27.5534259394694 40 259.6 284.552811498686 -24.9528114986862 41 241 257.13323658224 -16.1332365822401 42 230 252.843253277586 -22.8432532775859 43 230.3 253.479527390884 -23.1795273908840 44 214 236.721002362409 -22.7210023624091 45 202.9 235.500814384592 -32.6008143845918 46 188.5 208.879895340196 -20.3798953401960 47 215.6 238.069782624831 -22.4697826248305 48 205.6 213.926274941848 -8.32627494184792 49 203.7 182.996507546909 20.7034924530907 50 218.2 202.146551343265 16.0534486567349 51 253 234.893109492463 18.1068905075371 52 255.4 236.867144231277 18.5328557687226 53 240.7 244.690286441609 -3.99028644160937 54 242.2 253.636754823326 -11.4367548233264 55 240.2 228.130164443437 12.0698355565631 56 215.2 197.991309841044 17.2086901589555 57 211.1 183.093929697915 28.0060703020853 58 219.3 194.100648788609 25.1993512113909 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.00532914549351078 0.0106582909870216 0.99467085450649 10 0.00111757808067938 0.00223515616135877 0.99888242191932 11 0.00616843788604421 0.0123368757720884 0.993831562113956 12 0.00182257711730863 0.00364515423461726 0.998177422882691 13 0.00217607159019916 0.00435214318039831 0.9978239284098 14 0.000927708759081538 0.00185541751816308 0.999072291240918 15 0.00139434256328510 0.00278868512657021 0.998605657436715 16 0.000573104561948539 0.00114620912389708 0.999426895438051 17 0.000534038433410241 0.00106807686682048 0.99946596156659 18 0.00105402803443618 0.00210805606887236 0.998945971965564 19 0.00152489180677325 0.00304978361354650 0.998475108193227 20 0.00113141906909953 0.00226283813819905 0.9988685809309 21 0.00221934716343472 0.00443869432686945 0.997780652836565 22 0.00718974152662925 0.0143794830532585 0.99281025847337 23 0.0136281608910780 0.0272563217821559 0.986371839108922 24 0.0456134949679162 0.0912269899358323 0.954386505032084 25 0.0535143544890701 0.107028708978140 0.94648564551093 26 0.150833356006400 0.301666712012799 0.8491666439936 27 0.242940988503796 0.485881977007592 0.757059011496204 28 0.622743325011191 0.754513349977618 0.377256674988809 29 0.943236129951261 0.113527740097478 0.0567638700487391 30 0.99275871811484 0.0144825637703188 0.00724128188515939 31 0.99882233126465 0.00235533747070065 0.00117766873535032 32 0.999538177321642 0.000923645356715401 0.000461822678357701 33 0.999835236702289 0.000329526595421595 0.000164763297710798 34 0.999898358686889 0.000203282626222107 0.000101641313111053 35 0.999965967932403 6.80641351938378e-05 3.40320675969189e-05 36 0.999994440115787 1.11197684258296e-05 5.5598842129148e-06 37 0.999996428317466 7.14336506756025e-06 3.57168253378012e-06 38 0.999992726709848 1.4546580303717e-05 7.2732901518585e-06 39 0.999979723660035 4.05526799298561e-05 2.02763399649281e-05 40 0.999952224001057 9.55519978855357e-05 4.77759989427678e-05 41 0.99988904204907 0.000221915901860696 0.000110957950930348 42 0.99966929937631 0.000661401247379936 0.000330700623689968 43 0.999277511854484 0.00144497629103201 0.000722488145516006 44 0.997773128333933 0.00445374333213501 0.00222687166606751 45 0.993914411402538 0.0121711771949245 0.00608558859746225 46 0.983654613723856 0.0326907725522873 0.0163453862761437 47 0.992734958609408 0.0145300827811845 0.00726504139059227 48 0.996111763375728 0.00777647324854409 0.00388823662427204 49 0.981006930143564 0.0379861397128729 0.0189930698564365 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.634146341463415 NOK 5% type I error level 35 0.853658536585366 NOK 10% type I error level 36 0.878048780487805 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal 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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