*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: Sat, 19 Dec 2009 12:37:22 -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/19/t1261251488dj6k7p2e5yq4p2n.htm/, Retrieved Sat, 19 Dec 2009 20:38:20 +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/19/t1261251488dj6k7p2e5yq4p2n.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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19915 23322 19843 22558 19761 19185 20858 17869 21968 21515 23061 17686 22661 18044 22269 20398 21857 22894 21568 22016 21274 25325 20987 27683 19683 17333 19381 20190 19071 22589 20772 14588 22485 14296 24181 12237 23479 7607 22782 9303 22067 9226 21489 9351 20903 21266 20330 21377 19736 22034 19483 22483 19242 15122 20334 18982 21423 19653 22523 16653 21986 23528 21462 24612 20908 24733 20575 21839 20237 22421 19904 26543 19610 27067 19251 31403 18941 25762 20450 29359 21946 34174 23409 20163 22741 25226 22069 25077 21539 29764 21189 21372 20960 34136 20704 29126 19697 17279 19598 16163 19456 8058 20316 17888 21083 7642 22158 7458 21469 4639 20892 10276 20578 3129 20233 20023 19947 3744 20049 7848

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 X[t] = + 20145.6162252401 + 0.0110672595094855Y[t] -654.33304955969M1[t] -884.086959418418M2[t] -1052.21172797263M3[t] + 181.947060369252M4[t] + 1420.05917374332M5[t] + 2756.55228399481M6[t] + 2146.62368262631M7[t] + 1550.71239652436M8[t] + 1045.53532037221M9[t] + 655.789011388502M10[t] + 281.983474062285M11[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) 20145.6162252401 328.235737 61.3755 0 0 Y 0.0110672595094855 0.00987 1.1213 0.267852 0.133926 M1 -654.33304955969 341.802632 -1.9144 0.061673 0.030837 M2 -884.086959418418 341.627792 -2.5879 0.012808 0.006404 M3 -1052.21172797263 344.342218 -3.0557 0.003695 0.001847 M4 181.947060369252 342.726201 0.5309 0.598001 0.299 M5 1420.05917374332 342.959414 4.1406 0.000143 7.1e-05 M6 2756.55228399481 349.927368 7.8775 0 0 M7 2146.62368262631 347.981251 6.1688 0 0 M8 1550.71239652436 344.608104 4.4999 4.5e-05 2.2e-05 M9 1045.53532037221 344.587414 3.0342 0.003922 0.001961 M10 655.789011388502 343.465423 1.9093 0.062335 0.031167 M11 281.983474062285 341.811783 0.825 0.413558 0.206779 Multiple Linear Regression - Regression Statistics Multiple R 0.921689186463312 R-squared 0.849510956443402 Adjusted R-squared 0.811088221918313 F-TEST (value) 22.1095912860835 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 2.33146835171283e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 540.160530461654 Sum Squared Residuals 13713349.7374249 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 19915 19749.3938019607 165.606198039322 2 19843 19511.1845058367 331.815494163314 3 19761 19305.729870957 455.270129043018 4 20858 20525.3241457844 332.675854215621 5 21968 21803.7874873300 164.212512669968 6 23061 23097.9040609197 -36.9040609197011 7 22661 22491.9375384556 169.062461544398 8 22269 21922.078581239 346.921418761024 9 21857 21444.5253848225 412.474615177496 10 21568 21045.0620219895 522.937978010536 11 21274 20707.8780463801 566.121953619865 12 20987 20451.9911702412 535.008829758783 13 19683 19683.1119847584 -0.111984758352794 14 19381 19484.9772353182 -103.977235318225 15 19071 19343.4028223273 -272.402822327270 16 20772 20489.0124673338 282.987532666243 17 22485 21723.8929409311 761.107059068945 18 24181 23037.5985638525 1143.40143614749 19 23479 22376.4285509551 1102.57144904490 20 22782 21799.2873369812 982.71266301876 21 22067 21293.2580818469 773.741918153144 22 21489 20904.8951803018 584.104819698169 23 20903 20662.9560400311 240.043959968866 24 20330 20382.2010317744 -52.201031774402 25 19736 19735.1391717124 0.860828287555886 26 19483 19510.3544613735 -27.3544613734757 27 19242 19260.7635955699 -18.7635955699425 28 20334 20537.6420056184 -203.642005618437 29 21423 21783.1802501234 -360.180250123368 30 22523 23086.4715818464 -563.471581846403 31 21986 22552.6303896056 -566.63038960562 32 21462 21968.7160128120 -506.716012811952 33 20908 21464.8780750604 -556.878075060447 34 20575 21043.1031170563 -468.103117056286 35 20237 20675.7387247646 -438.73872476459 36 19904 20439.3744944004 -535.374494400404 37 19610 19790.8406888237 -180.840688823685 38 19251 19609.0744161981 -358.074416198086 39 18941 19378.5192367509 -437.519236750868 40 20450 20652.4869575484 -202.486957548367 41 21946 21943.8879254606 2.11207453939287 42 23409 23125.3176627247 283.682337275302 43 22741 22571.4225962527 169.577403747273 44 22069 21973.8622884839 95.1377115161368 45 21539 21520.5574576527 18.4425423473310 46 21189 21037.9347068654 151.065293134643 47 20960 20805.3916699182 154.608330081788 48 20704 20467.9612257134 236.038774286595 49 19697 19682.5143527448 14.4856472551593 50 19598 19440.4093812735 157.590618726473 51 19456 19182.5844743949 273.415525605063 52 20316 20525.5344237151 -209.534423715059 53 21083 21650.2513961549 -567.251396154938 54 22158 22984.7081306567 -826.708130656684 55 21469 22343.5809247309 -874.58092473095 56 20892 21810.0557804840 -918.055780483969 57 20578 21225.7810006175 -647.781000617523 58 20233 21023.0049737871 -790.00497378706 59 19947 20469.0355189059 -522.03551890593 60 20049 20232.4720778706 -183.472077870573 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.203515612212608 0.407031224425216 0.796484387787392 17 0.143590916243489 0.287181832486978 0.856409083756511 18 0.260701405463485 0.521402810926969 0.739298594536515 19 0.238641570910938 0.477283141821875 0.761358429089062 20 0.265374787682064 0.530749575364127 0.734625212317936 21 0.380142795204999 0.760285590409999 0.619857204795 22 0.549990701128292 0.900018597743416 0.450009298871708 23 0.556665617010602 0.886668765978797 0.443334382989398 24 0.629398030395664 0.741203939208672 0.370601969604336 25 0.528312025092033 0.943375949815934 0.471687974907967 26 0.430032348274656 0.860064696549312 0.569967651725344 27 0.362129012600575 0.72425802520115 0.637870987399425 28 0.317236807977903 0.634473615955805 0.682763192022097 29 0.364619290198936 0.729238580397871 0.635380709801064 30 0.514021187423034 0.971957625153932 0.485978812576966 31 0.525617331413261 0.948765337173479 0.474382668586739 32 0.497383323563088 0.994766647126176 0.502616676436912 33 0.481308733251552 0.962617466503104 0.518691266748448 34 0.435692199789821 0.871384399579642 0.564307800210179 35 0.451411625475692 0.902823250951384 0.548588374524308 36 0.500274059855335 0.99945188028933 0.499725940144665 37 0.424839460784545 0.84967892156909 0.575160539215455 38 0.459994373354276 0.919988746708552 0.540005626645724 39 0.68730401088664 0.625391978226721 0.312695989113361 40 0.623246377465244 0.753507245069513 0.376753622534756 41 0.564566050972284 0.870867898055432 0.435433949027716 42 0.59323937085481 0.81352125829038 0.40676062914519 43 0.521054903271631 0.957890193456739 0.478945096728369 44 0.524715187002824 0.950569625994352 0.475284812997176 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 = 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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