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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: Thu, 27 Nov 2008 05:56:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227791363iy4z5fo42ueeely.htm/, Retrieved Thu, 27 Nov 2008 13:09:33 +0000

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/2008/Nov/27/t1227791363iy4z5fo42ueeely.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

kleuter

Dataseries X:

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104,3 0 119,8 0 116,8 0 118,2 0 107,4 0 110,8 0 94,8 0 96,5 0 113,4 0 109,8 0 118,7 0 117,2 0 110,3 0 111,6 0 128,1 0 121,3 0 107,3 0 120,5 0 98,5 0 97,7 0 113,2 0 114,6 0 118,3 0 123,9 0 113,6 0 117,5 0 130,1 0 124,7 0 114,2 0 127,3 0 105,9 0 101,5 0 120,2 0 117,1 0 131,1 0 130 0 120,6 0 123,1 0 135,3 0 134,1 0 123,7 0 134,6 0 108,3 1 110,4 1 127,8 1 126,6 1 131,4 1 141,1 1 127 1 127,3 1 143,6 1 149,4 1 126,6 1 136,5 1 116 1 118 1 131,4 1 140,7 1 144,9 1 143,9 1 127,1 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation x[t] = + 116.609523809524 + 13.8115288220551y[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) 116.609523809524 1.68277 69.2962 0 0 y 13.8115288220551 3.015177 4.5807 2.4e-05 1.2e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.512190311264372 R-squared 0.262338914953094 Adjusted R-squared 0.249836184698062 F-TEST (value) 20.9825301835576 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 2.44823599915289e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.9055947151875 Sum Squared Residuals 7016.98776942355 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.3 116.609523809524 -12.3095238095237 2 119.8 116.609523809524 3.19047619047618 3 116.8 116.609523809524 0.190476190476185 4 118.2 116.609523809524 1.59047619047619 5 107.4 116.609523809524 -9.2095238095238 6 110.8 116.609523809524 -5.80952380952382 7 94.8 116.609523809524 -21.8095238095238 8 96.5 116.609523809524 -20.1095238095238 9 113.4 116.609523809524 -3.20952380952381 10 109.8 116.609523809524 -6.80952380952382 11 118.7 116.609523809524 2.09047619047619 12 117.2 116.609523809524 0.59047619047619 13 110.3 116.609523809524 -6.30952380952382 14 111.6 116.609523809524 -5.00952380952382 15 128.1 116.609523809524 11.4904761904762 16 121.3 116.609523809524 4.69047619047618 17 107.3 116.609523809524 -9.30952380952382 18 120.5 116.609523809524 3.89047619047619 19 98.5 116.609523809524 -18.1095238095238 20 97.7 116.609523809524 -18.9095238095238 21 113.2 116.609523809524 -3.40952380952381 22 114.6 116.609523809524 -2.00952380952382 23 118.3 116.609523809524 1.69047619047618 24 123.9 116.609523809524 7.2904761904762 25 113.6 116.609523809524 -3.00952380952382 26 117.5 116.609523809524 0.890476190476188 27 130.1 116.609523809524 13.4904761904762 28 124.7 116.609523809524 8.0904761904762 29 114.2 116.609523809524 -2.40952380952381 30 127.3 116.609523809524 10.6904761904762 31 105.9 116.609523809524 -10.7095238095238 32 101.5 116.609523809524 -15.1095238095238 33 120.2 116.609523809524 3.59047619047619 34 117.1 116.609523809524 0.490476190476182 35 131.1 116.609523809524 14.4904761904762 36 130 116.609523809524 13.3904761904762 37 120.6 116.609523809524 3.99047619047618 38 123.1 116.609523809524 6.49047619047618 39 135.3 116.609523809524 18.6904761904762 40 134.1 116.609523809524 17.4904761904762 41 123.7 116.609523809524 7.0904761904762 42 134.6 116.609523809524 17.9904761904762 43 108.3 130.421052631579 -22.1210526315790 44 110.4 130.421052631579 -20.0210526315789 45 127.8 130.421052631579 -2.62105263157895 46 126.6 130.421052631579 -3.82105263157895 47 131.4 130.421052631579 0.97894736842106 48 141.1 130.421052631579 10.6789473684210 49 127 130.421052631579 -3.42105263157895 50 127.3 130.421052631579 -3.12105263157895 51 143.6 130.421052631579 13.1789473684210 52 149.4 130.421052631579 18.9789473684211 53 126.6 130.421052631579 -3.82105263157895 54 136.5 130.421052631579 6.07894736842105 55 116 130.421052631579 -14.4210526315789 56 118 130.421052631579 -12.4210526315789 57 131.4 130.421052631579 0.97894736842106 58 140.7 130.421052631579 10.2789473684210 59 144.9 130.421052631579 14.4789473684211 60 143.9 130.421052631579 13.4789473684211 61 127.1 130.421052631579 -3.32105263157895 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.327911979442982 0.655823958885965 0.672088020557018 6 0.18754720495889 0.37509440991778 0.81245279504111 7 0.448329921598094 0.896659843196189 0.551670078401906 8 0.537490436143267 0.925019127713466 0.462509563856733 9 0.43658379603495 0.8731675920699 0.56341620396505 10 0.332982198298761 0.665964396597523 0.667017801701238 11 0.304118987579721 0.608237975159442 0.695881012420279 12 0.25066843176644 0.50133686353288 0.74933156823356 13 0.182134074756515 0.364268149513029 0.817865925243485 14 0.127593601243967 0.255187202487933 0.872406398756033 15 0.225635188613521 0.451270377227041 0.77436481138648 16 0.203306208038939 0.406612416077878 0.796693791961061 17 0.169954194601027 0.339908389202053 0.830045805398973 18 0.144595988794031 0.289191977588063 0.855404011205969 19 0.2250892750776 0.4501785501552 0.7749107249224 20 0.348098420200671 0.696196840401342 0.651901579799329 21 0.291591514588439 0.583183029176878 0.708408485411561 22 0.240925465242342 0.481850930484683 0.759074534757658 23 0.203809468359831 0.407618936719663 0.796190531640169 24 0.204351571573199 0.408703143146398 0.7956484284268 25 0.166091799524883 0.332183599049766 0.833908200475117 26 0.133534148094434 0.267068296188867 0.866465851905566 27 0.185784675781691 0.371569351563382 0.814215324218309 28 0.175030269715808 0.350060539431616 0.824969730284192 29 0.141559998583426 0.283119997166851 0.858440001416574 30 0.145919792932833 0.291839585865665 0.854080207067167 31 0.171705532026553 0.343411064053105 0.828294467973447 32 0.306884881850163 0.613769763700326 0.693115118149837 33 0.272886068341933 0.545772136683867 0.727113931658067 34 0.253618843603579 0.507237687207158 0.746381156396421 35 0.280791153668089 0.561582307336177 0.719208846331912 36 0.284896975945244 0.569793951890488 0.715103024054756 37 0.254633035967866 0.509266071935732 0.745366964032134 38 0.229611774111799 0.459223548223599 0.7703882258882 39 0.264082586662194 0.528165173324388 0.735917413337806 40 0.27596695853234 0.55193391706468 0.72403304146766 41 0.241733092889544 0.483466185779088 0.758266907110456 42 0.238114873161888 0.476229746323775 0.761885126838112 43 0.362311627797695 0.72462325559539 0.637688372202305 44 0.533505026586021 0.932989946827958 0.466494973413979 45 0.506991110970854 0.986017778058292 0.493008889029146 46 0.462886502516306 0.925773005032611 0.537113497483694 47 0.39982213786703 0.79964427573406 0.60017786213297 48 0.396809301671113 0.793618603342225 0.603190698328887 49 0.330494045765462 0.660988091530924 0.669505954234538 50 0.268487457295291 0.536974914590583 0.731512542704709 51 0.267946658349104 0.535893316698207 0.732053341650896 52 0.398225025921877 0.796450051843753 0.601774974078124 53 0.307592806939223 0.615185613878447 0.692407193060777 54 0.220182924706596 0.440365849413193 0.779817075293404 55 0.321871515407628 0.643743030815256 0.678128484592372 56 0.553223361043474 0.893553277913053 0.446776638956526 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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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