ws10 multiple regression

*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 23:42:00 +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/15/t1292370318rezcvqndls2sk1w.htm/, Retrieved Wed, 15 Dec 2010 00:45:27 +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/15/t1292370318rezcvqndls2sk1w.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:

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Dataseries X:

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0.504208603 0.397232704 0.457969746 0.382767296 0.509923035 0.396037736 0.606622221 0.441761006 0.626210885 0.445220126 0.626631316 0.438490566 0.676731276 0.467484277 0.613117455 0.465786164 0.486215861 0.402075472 0.452529881 0.376163522 0.467150592 0.37591195 0.494624486 0.392955975 0.444567428 0.34490566 0.478862605 0.368553459 0.544458459 0.390880503 0.628201498 0.424842767 0.672578445 0.426855346 0.652706633 0.442327044 0.645430599 0.474842767 0.576334011 0.447610063 0.618334234 0.480754717 0.639896351 0.516037736 0.72850438 0.580628931 0.694655375 0.573522013 0.689773225 0.578867925 0.712244845 0.593584906 0.760337031 0.645974843 0.837816503 0.690503145 0.90688735 0.782201258 0.976018259 0.839056604 0.962066806 0.847484277 0.837593417 0.726855346 0.767638807 0.635534591 0.580006349 0.470943396 0.387740568 0.346163522 0.331274078 0.272327044 0.345251272 0.286792453 0.380172806 0.27672956 0.399838692 0.297421384 0.425742404 0.321698113 0.524183377 0.365597484 0.59 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation olie[t] = -0.0541370250440066 + 0.879652544184293benzine[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) -0.0541370250440066 0.02054 -2.6357 0.010798 0.005399 benzine 0.879652544184293 0.033264 26.4442 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.961578230829939 R-squared 0.924632694006035 Adjusted R-squared 0.923310460567544 F-TEST (value) 699.296105430171 F-TEST (DF numerator) 1 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0344242198136767 Sum Squared Residuals 0.0675465338574791 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.397232704 0.389391355384552 0.00784134861544753 2 0.382767296 0.348717227184328 0.034050068815672 3 0.396037736 0.39441807003192 0.00161966596808033 4 0.441761006 0.47947975501737 -0.0377187490173697 5 0.445220126 0.496710973142141 -0.051490847142141 6 0.438490566 0.497080806340945 -0.0585902403409449 7 0.467484277 0.541151363618476 -0.0736670866184763 8 0.465786164 0.485193304130542 -0.0194071401305421 9 0.402075472 0.3735639941074 0.0285114778926001 10 0.376163522 0.343932036097059 0.0322314859029412 11 0.37591195 0.356793181725992 0.0191187682740080 12 0.392955975 0.380960662481742 0.0119953125182585 13 0.34490566 0.336927844057661 0.00797781594233914 14 0.368553459 0.367095683758962 0.00145777524103854 15 0.390880503 0.424797243618003 -0.0339167406180029 16 0.424842767 0.498462020932077 -0.0736192539320773 17 0.426855346 0.537498315263759 -0.110642969263759 18 0.442327044 0.520018025280407 -0.0776909812804069 19 0.474842767 0.513617643460735 -0.0387748764607355 20 0.447610063 0.452836654032082 -0.00522659103208164 21 0.480754717 0.489782257050339 -0.00902754005033924 22 0.516037736 0.508749428127389 0.00728830787261142 23 0.580628931 0.586693706272394 -0.00606477527239415 24 0.573522013 0.556918342906037 0.0166036700939627 25 0.578867925 0.552623747237448 0.0262441777625519 26 0.593584906 0.57239096494239 0.0211939410576094 27 0.645974843 0.614695378712675 0.0312794642873251 28 0.690503145 0.68285039337953 0.00765275162046947 29 0.782201258 0.743608739672045 0.0385925183279554 30 0.839056604 0.804419919655667 0.0346366843443327 31 0.847484277 0.79214748852915 0.0553367884708501 32 0.726855346 0.682654155212059 0.0442011907879414 33 0.635534591 0.621118404548139 0.0144161864518613 34 0.470943396 0.456067035496886 0.0148763605031137 35 0.346163522 0.286939952080656 0.0592235699193437 36 0.272327044 0.237269060490999 0.0350579835090006 37 0.286792453 0.249564134753657 0.0372283182463432 38 0.27672956 0.280282950983575 -0.00355339098357503 39 0.297421384 0.297582097637113 -0.000160713637113282 40 0.321698113 0.320368363801731 0.00132974919826951 41 0.365597484 0.406962216153158 -0.0413647321531577 42 0.435220126 0.471116991522979 -0.0358968655229794 43 0.412893082 0.42218576633093 -0.0092926843309303 44 0.458679245 0.486883970810540 -0.0282047258105404 45 0.428427673 0.427846482632646 0.000581190367353649 46 0.463522013 0.451259201273477 0.0122628117265227 47 0.487169811 0.476679587861307 0.0104902231386931 48 0.473584906 0.453855582843239 0.0197293231567609 49 0.491886792 0.486144304412933 0.00574248758706747 50 0.474842767 0.460263512961392 0.0145792540386078 51 0.502327044 0.497865759010833 0.00446128498916738 52 0.539371069 0.54126457753987 -0.00189350853987035 53 0.484402516 0.514115786298244 -0.0297132702982443 54 0.474654088 0.470188634376729 0.00446545362327133 55 0.473522013 0.461305084908690 0.0122169280913104 56 0.48754717 0.480355279352164 0.00719189064783578 57 0.493333333 0.47230196794664 0.0210313650533602 58 0.525157233 0.507700308761262 0.0174569242387378 59 0.542704403 0.516961238846934 0.0257431641530657 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00159452722528739 0.00318905445057478 0.998405472774713 6 0.000642352009735451 0.00128470401947090 0.999357647990265 7 0.000139159194790768 0.000278318389581536 0.99986084080521 8 0.00439265244093757 0.00878530488187514 0.995607347559062 9 0.00186042070749849 0.00372084141499699 0.998139579292502 10 0.000607787235261097 0.00121557447052219 0.999392212764739 11 0.000248597573499634 0.000497195146999269 0.9997514024265 12 6.82521151268311e-05 0.000136504230253662 0.999931747884873 13 0.00035007236655416 0.00070014473310832 0.999649927633446 14 0.000225900674042520 0.000451801348085041 0.999774099325957 15 0.000294599651775336 0.000589199303550672 0.999705400348225 16 0.000742853132310907 0.00148570626462181 0.99925714686769 17 0.0177375654125673 0.0354751308251345 0.982262434587433 18 0.0446724020603833 0.0893448041207665 0.955327597939617 19 0.101653526993022 0.203307053986044 0.898346473006978 20 0.122376620212941 0.244753240425881 0.87762337978706 21 0.236896919421017 0.473793838842035 0.763103080578983 22 0.561685534354998 0.876628931290005 0.438314465645002 23 0.861414818788528 0.277170362422945 0.138585181211472 24 0.948033856997288 0.103932286005423 0.0519661430027116 25 0.97822171292094 0.0435565741581187 0.0217782870790594 26 0.986331937410138 0.0273361251797244 0.0136680625898622 27 0.993104464175976 0.0137910716480488 0.00689553582402439 28 0.992794237873755 0.0144115242524899 0.00720576212624494 29 0.995192226175485 0.0096155476490301 0.00480777382451505 30 0.99480290327592 0.0103941934481583 0.00519709672407916 31 0.997949089383925 0.00410182123215089 0.00205091061607544 32 0.999242002578003 0.00151599484399343 0.000757997421996713 33 0.998970677077536 0.00205864584492851 0.00102932292246426 34 0.998273335267447 0.00345332946510543 0.00172666473255271 35 0.999579288705709 0.000841422588582937 0.000420711294291468 36 0.999547137980543 0.000905724038913794 0.000452862019456897 37 0.999749975531723 0.00050004893655356 0.00025002446827678 38 0.999437356497241 0.00112528700551772 0.000562643502758862 39 0.998820539627554 0.00235892074489280 0.00117946037244640 40 0.997854732990786 0.00429053401842757 0.00214526700921378 41 0.99912868886791 0.00174262226418179 0.000871311132090893 42 0.999775117237146 0.000449765525707804 0.000224882762853902 43 0.99968517099125 0.000629658017498337 0.000314829008749169 44 0.99992709949412 0.000145801011761555 7.29005058807774e-05 45 0.9998834327027 0.000233134594599897 0.000116567297299948 46 0.999654089032257 0.000691821935485234 0.000345910967742617 47 0.99898701080627 0.00202597838746045 0.00101298919373023 48 0.99735289504334 0.00529420991332081 0.00264710495666040 49 0.993039191486698 0.0139216170266035 0.00696080851330173 50 0.98272150974519 0.0345569805096199 0.0172784902548099 51 0.959549234357649 0.0809015312847026 0.0404507656423513 52 0.911542296102803 0.176915407794394 0.088457703897197 53 0.99698110308385 0.00603779383229997 0.00301889691614998 54 0.990426636265006 0.0191467274699877 0.00957336373499386 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 32 0.64 NOK 5% type I error level 41 0.82 NOK 10% type I error level 43 0.86 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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