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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: Sat, 05 Dec 2009 17:58:02 -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/06/t12600611223joh8467d43csx8.htm/, Retrieved Sun, 06 Dec 2009 01:58:53 +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/06/t12600611223joh8467d43csx8.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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No (this computation is public)

User-defined keywords:

Dataseries X:

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100.00 0 100.83 0 101.51 0 102.16 0 102.39 0 102.54 0 102.85 0 103.47 0 103.57 0 103.69 0 103.50 0 103.47 0 103.45 0 103.48 0 103.93 0 103.89 0 104.40 0 104.79 0 104.77 0 105.13 0 105.26 0 104.96 0 104.75 0 105.01 0 105.15 0 105.20 0 105.77 0 105.78 0 106.26 0 106.13 0 106.12 0 106.57 0 106.44 0 106.54 0 107.10 0 108.10 0 108.40 0 108.84 0 109.62 0 110.42 0 110.67 0 111.66 0 112.28 0 112.87 1 112.18 1 112.36 1 112.16 1 111.49 1 111.25 1 111.36 1 111.74 1 111.10 1 111.33 1 111.25 1 111.04 1 110.97 1 111.31 1 111.02 1 111.07 1 111.36 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 100.798537205082 + 0.405499092558974X[t] -0.0388475499092781M1[t] + 0.0607840290381172M2[t] + 0.440415607985486M3[t] + 0.404047186932851M4[t] + 0.551678765880222M5[t] + 0.62331034482759M6[t] + 0.568941923774957M7[t] + 0.685473684210528M8[t] + 0.443105263157899M9[t] + 0.212736842105264M10[t] + 0.0223684210526305M11[t] + 0.192368421052632t + 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) 100.798537205082 0.643474 156.6474 0 0 X 0.405499092558974 0.550092 0.7371 0.464776 0.232388 M1 -0.0388475499092781 0.752095 -0.0517 0.959029 0.479515 M2 0.0607840290381172 0.750878 0.081 0.935832 0.467916 M3 0.440415607985486 0.749931 0.5873 0.559891 0.279945 M4 0.404047186932851 0.749254 0.5393 0.592304 0.296152 M5 0.551678765880222 0.748847 0.7367 0.465043 0.232521 M6 0.62331034482759 0.748711 0.8325 0.409422 0.204711 M7 0.568941923774957 0.748847 0.7598 0.451276 0.225638 M8 0.685473684210528 0.747681 0.9168 0.36403 0.182015 M9 0.443105263157899 0.74673 0.5934 0.555824 0.277912 M10 0.212736842105264 0.746049 0.2852 0.776808 0.388404 M11 0.0223684210526305 0.745641 0.03 0.976198 0.488099 t 0.192368421052632 0.014253 13.4971 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.958777964425264 R-squared 0.919255185067454 Adjusted R-squared 0.89643599823869 F-TEST (value) 40.2843095139899 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.17874632783709 Sum Squared Residuals 63.9143736479132 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100 100.952058076225 -0.952058076225158 2 100.83 101.244058076225 -0.414058076225041 3 101.51 101.816058076225 -0.306058076225035 4 102.16 101.972058076225 0.187941923774961 5 102.39 102.312058076225 0.0779419237749595 6 102.54 102.576058076225 -0.0360580762250324 7 102.85 102.714058076225 0.135941923774957 8 103.47 103.022958257713 0.447041742286757 9 103.57 102.972958257713 0.597041742286748 10 103.69 102.934958257713 0.755041742286756 11 103.5 102.936958257713 0.56304174228676 12 103.47 103.106958257713 0.363041742286757 13 103.45 103.260479128857 0.189520871143408 14 103.48 103.552479128857 -0.0724791288566186 15 103.93 104.124479128857 -0.194479128856616 16 103.89 104.280479128857 -0.390479128856619 17 104.4 104.620479128857 -0.220479128856618 18 104.79 104.884479128857 -0.094479128856616 19 104.77 105.022479128857 -0.252479128856626 20 105.13 105.331379310345 -0.201379310344829 21 105.26 105.281379310345 -0.0213793103448229 22 104.96 105.243379310345 -0.283379310344831 23 104.75 105.245379310345 -0.495379310344823 24 105.01 105.415379310345 -0.40537931034482 25 105.15 105.568900181488 -0.418900181488173 26 105.2 105.860900181488 -0.660900181488204 27 105.77 106.432900181488 -0.66290018148821 28 105.78 106.588900181488 -0.808900181488202 29 106.26 106.928900181488 -0.668900181488202 30 106.13 107.192900181488 -1.06290018148821 31 106.12 107.330900181488 -1.2109001814882 32 106.57 107.639800362976 -1.06980036297642 33 106.44 107.589800362976 -1.14980036297641 34 106.54 107.551800362976 -1.01180036297640 35 107.1 107.553800362976 -0.453800362976413 36 108.1 107.723800362976 0.376199637023586 37 108.4 107.877321234120 0.522678765880243 38 108.84 108.169321234120 0.670678765880211 39 109.62 108.741321234120 0.878678765880214 40 110.42 108.897321234120 1.52267876588021 41 110.67 109.237321234120 1.43267876588021 42 111.66 109.501321234120 2.15867876588021 43 112.28 109.639321234120 2.64067876588021 44 112.87 110.353720508167 2.51627949183304 45 112.18 110.303720508167 1.87627949183304 46 112.36 110.265720508167 2.09427949183303 47 112.16 110.267720508167 1.89227949183303 48 111.49 110.437720508167 1.05227949183303 49 111.25 110.591241379310 0.65875862068968 50 111.36 110.883241379310 0.476758620689652 51 111.74 111.455241379310 0.284758620689648 52 111.1 111.611241379310 -0.511241379310351 53 111.33 111.951241379310 -0.62124137931035 54 111.25 112.215241379310 -0.965241379310347 55 111.04 112.353241379310 -1.31324137931034 56 110.97 112.662141560799 -1.69214156079855 57 111.31 112.612141560799 -1.30214156079855 58 111.02 112.574141560799 -1.55414156079855 59 111.07 112.576141560799 -1.50614156079856 60 111.36 112.746141560799 -1.38614156079855 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0655361078415911 0.131072215683182 0.93446389215841 18 0.0199162322565396 0.0398324645130791 0.98008376774346 19 0.00685330366418644 0.0137066073283729 0.993146696335814 20 0.00292715651676128 0.00585431303352256 0.997072843483239 21 0.00107540158264470 0.00215080316528941 0.998924598417355 22 0.000673722262188697 0.00134744452437739 0.999326277737811 23 0.000362910149662034 0.000725820299324068 0.999637089850338 24 0.000122697350820348 0.000245394701640696 0.99987730264918 25 4.24735365985779e-05 8.49470731971557e-05 0.999957526463401 26 1.19812274245535e-05 2.39624548491069e-05 0.999988018772575 27 3.38997248688998e-06 6.77994497377996e-06 0.999996610027513 28 1.18071988136748e-06 2.36143976273496e-06 0.999998819280119 29 3.72306159309784e-07 7.44612318619569e-07 0.99999962769384 30 3.05555619232664e-07 6.11111238465327e-07 0.999999694444381 31 7.07883400666634e-07 1.41576680133327e-06 0.9999992921166 32 9.30244008912707e-07 1.86048801782541e-06 0.999999069755991 33 3.22144775638634e-06 6.44289551277268e-06 0.999996778552244 34 1.69609052481110e-05 3.39218104962219e-05 0.999983039094752 35 0.000150545450654069 0.000301090901308138 0.999849454549346 36 0.00345949563950515 0.00691899127901031 0.996540504360495 37 0.0469715196907015 0.093943039381403 0.953028480309299 38 0.231952029139728 0.463904058279456 0.768047970860272 39 0.655841565506043 0.688316868987914 0.344158434493957 40 0.767386403866493 0.465227192267014 0.232613596133507 41 0.885330294221173 0.229339411557653 0.114669705778827 42 0.885821276997156 0.228357446005688 0.114178723002844 43 0.821134181206357 0.357731637587286 0.178865818793643 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 17 0.62962962962963 NOK 5% type I error level 19 0.703703703703704 NOK 10% type I error level 20 0.740740740740741 NOK

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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