*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 09:39:43 -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/t12612409128vejl41tbrhpqac.htm/, Retrieved Sat, 19 Dec 2009 17:42:05 +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/t12612409128vejl41tbrhpqac.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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101.09 0 102.71 0 102.11 0 101.68 0 101.7 0 101.53 0 101.76 0 101.15 0 100.92 0 100.73 0 100.55 0 102.15 0 100.79 0 99.93 0 100.03 0 100.25 0 99.6 0 100.16 0 100.49 0 99.72 0 100.14 0 98.48 0 100.38 0 101.45 0 98.42 0 98.6 0 100.06 0 98.62 0 100.84 0 100.02 0 97.95 0 98.32 0 98.27 0 97.22 0 99.28 0 100.38 0 99.02 0 100.32 0 99.81 0 100.6 0 101.19 0 100.47 0 101.77 0 102.32 0 102.39 0 101.16 0 100.63 0 101.48 0 101.44 1 100.09 1 100.7 1 100.78 1 99.81 1 98.45 1 98.49 1 97.48 1 97.91 1 96.94 1 98.53 1 96.82 1 95.76 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 100.785684210526 -1.64842105263159X[t] -0.816210526315732M1[t] -0.126M2[t] + 0.0860000000000034M3[t] -0.0699999999999973M4[t] + 0.172000000000002M5[t] -0.330000000000000M6[t] -0.364M7[t] -0.658M8[t] -0.529999999999999M9[t] -1.55000000000000M10[t] -0.582000000000001M11[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) 100.785684210526 0.654317 154.0319 0 0 X -1.64842105263159 0.455148 -3.6217 0.000704 0.000352 M1 -0.816210526315732 0.87943 -0.9281 0.357993 0.178996 M2 -0.126 0.916345 -0.1375 0.891209 0.445604 M3 0.0860000000000034 0.916345 0.0939 0.925618 0.462809 M4 -0.0699999999999973 0.916345 -0.0764 0.939426 0.469713 M5 0.172000000000002 0.916345 0.1877 0.851901 0.425951 M6 -0.330000000000000 0.916345 -0.3601 0.720333 0.360166 M7 -0.364 0.916345 -0.3972 0.692959 0.346479 M8 -0.658 0.916345 -0.7181 0.476195 0.238097 M9 -0.529999999999999 0.916345 -0.5784 0.565708 0.282854 M10 -1.55000000000000 0.916345 -1.6915 0.097224 0.048612 M11 -0.582000000000001 0.916345 -0.6351 0.528359 0.264179 Multiple Linear Regression - Regression Statistics Multiple R 0.540955008842867 R-squared 0.292632321592186 Adjusted R-squared 0.115790401990232 F-TEST (value) 1.65476784153249 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.107998708785458 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.44886891758740 Sum Squared Residuals 100.762614736843 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.09 99.9694736842103 1.12052631578974 2 102.71 100.659684210526 2.05031578947367 3 102.11 100.871684210526 1.23831578947368 4 101.68 100.715684210526 0.964315789473686 5 101.7 100.957684210526 0.742315789473685 6 101.53 100.455684210526 1.07431578947369 7 101.76 100.421684210526 1.33831578947369 8 101.15 100.127684210526 1.02231578947369 9 100.92 100.255684210526 0.664315789473684 10 100.73 99.2356842105263 1.49431578947369 11 100.55 100.203684210526 0.346315789473681 12 102.15 100.785684210526 1.36431578947369 13 100.79 99.9694736842106 0.820526315789422 14 99.93 100.659684210526 -0.72968421052631 15 100.03 100.871684210526 -0.841684210526319 16 100.25 100.715684210526 -0.465684210526320 17 99.6 100.957684210526 -1.35768421052632 18 100.16 100.455684210526 -0.295684210526320 19 100.49 100.421684210526 0.0683157894736786 20 99.72 100.127684210526 -0.407684210526318 21 100.14 100.255684210526 -0.115684210526316 22 98.48 99.2356842105263 -0.755684210526314 23 100.38 100.203684210526 0.17631578947368 24 101.45 100.785684210526 0.664315789473686 25 98.42 99.9694736842106 -1.54947368421058 26 98.6 100.659684210526 -2.05968421052632 27 100.06 100.871684210526 -0.811684210526318 28 98.62 100.715684210526 -2.09568421052631 29 100.84 100.957684210526 -0.117684210526315 30 100.02 100.455684210526 -0.435684210526321 31 97.95 100.421684210526 -2.47168421052631 32 98.32 100.127684210526 -1.80768421052632 33 98.27 100.255684210526 -1.98568421052632 34 97.22 99.2356842105263 -2.01568421052632 35 99.28 100.203684210526 -0.923684210526314 36 100.38 100.785684210526 -0.405684210526321 37 99.02 99.9694736842106 -0.949473684210588 38 100.32 100.659684210526 -0.339684210526323 39 99.81 100.871684210526 -1.06168421052632 40 100.6 100.715684210526 -0.115684210526325 41 101.19 100.957684210526 0.232315789473680 42 100.47 100.455684210526 0.0143157894736818 43 101.77 100.421684210526 1.34831578947368 44 102.32 100.127684210526 2.19231578947368 45 102.39 100.255684210526 2.13431578947368 46 101.16 99.2356842105263 1.92431578947368 47 100.63 100.203684210526 0.42631578947368 48 101.48 100.785684210526 0.694315789473687 49 101.44 98.321052631579 3.11894736842100 50 100.09 99.0112631578947 1.07873684210528 51 100.7 99.2232631578947 1.47673684210527 52 100.78 99.0672631578947 1.71273684210527 53 99.81 99.3092631578947 0.500736842105274 54 98.45 98.8072631578947 -0.357263157894725 55 98.49 98.7732631578947 -0.283263157894732 56 97.48 98.4792631578947 -0.999263157894724 57 97.91 98.6072631578947 -0.697263157894731 58 96.94 97.5872631578947 -0.647263157894732 59 98.53 98.5552631578947 -0.0252631578947256 60 96.82 99.1372631578947 -2.31726315789473 61 95.76 98.321052631579 -2.56105263157899 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.59255879106684 0.81488241786632 0.40744120893316 17 0.560863756829613 0.878272486340774 0.439136243170387 18 0.45803912230002 0.91607824460004 0.54196087769998 19 0.363268014783922 0.726536029567844 0.636731985216078 20 0.289604549678118 0.579209099356236 0.710395450321882 21 0.201944009022416 0.403888018044832 0.798055990977584 22 0.200251351583034 0.400502703166067 0.799748648416966 23 0.129759806769463 0.259519613538926 0.870240193230537 24 0.0890528125618273 0.178105625123655 0.910947187438173 25 0.121439802336477 0.242879604672953 0.878560197663523 26 0.177435088965266 0.354870177930531 0.822564911034734 27 0.132064928504199 0.264129857008397 0.867935071495801 28 0.171539903257169 0.343079806514338 0.828460096742831 29 0.116420674902892 0.232841349805785 0.883579325097108 30 0.0793032474405708 0.158606494881142 0.92069675255943 31 0.150787487952337 0.301574975904674 0.849212512047663 32 0.168152856542912 0.336305713085823 0.831847143457088 33 0.208549085640287 0.417098171280575 0.791450914359713 34 0.264837282839322 0.529674565678644 0.735162717160678 35 0.219552695842214 0.439105391684428 0.780447304157786 36 0.166608264982316 0.333216529964632 0.833391735017684 37 0.142655269878261 0.285310539756523 0.857344730121739 38 0.117164884064768 0.234329768129536 0.882835115935232 39 0.155198953314115 0.31039790662823 0.844801046685885 40 0.191936984021553 0.383873968043105 0.808063015978447 41 0.167674617453484 0.335349234906969 0.832325382546516 42 0.129910812003776 0.259821624007552 0.870089187996224 43 0.0882041088964039 0.176408217792808 0.911795891103596 44 0.0654675542858985 0.130935108571797 0.934532445714101 45 0.0415976913344129 0.0831953826688259 0.958402308665587 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 1 0.0333333333333333 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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