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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: Mon, 24 Nov 2008 06:22:49 -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/24/t1227533035kp2e3xvzoc4nwag.htm/, Retrieved Mon, 24 Nov 2008 13:24:06 +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/24/t1227533035kp2e3xvzoc4nwag.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:

Dataseries X:

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9097 0 12639 0 13040 0 11687 0 11191 0 11391 0 11793 0 13933 0 12778 0 11810 0 13698 0 11956 0 10723 0 13938 0 13979 0 13807 0 12973 0 12509 0 12934 0 14908 0 13772 0 13012 0 14049 0 11816 0 11593 0 14466 0 13615 0 14733 0 13880 0 13527 0 13584 0 16170 0 13260 0 14741 0 15486 0 13154 0 12621 0 15031 0 15452 0 15428 0 13105 0 14716 0 14180 0 16202 0 14392 0 15140 0 15960 0 14351 0 13230 0 15202 0 17157 1 16159 1 13405 1 17224 1 17338 1 17370 1 18817 1 16593 1 17979 1 17015 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 Uitvoer[t] = + 13533.04 + 3372.66x[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) 13533.04 210.176538 64.3889 0 0 x 3372.66 514.825275 6.5511 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.652125791064754 R-squared 0.425268047371832 Adjusted R-squared 0.415358875774794 F-TEST (value) 42.9166094468459 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.65659783668559e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1486.17255472364 Sum Squared Residuals 128105114.02 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9097 13533.04 -4436.04 2 12639 13533.04 -894.039999999998 3 13040 13533.04 -493.04 4 11687 13533.04 -1846.04 5 11191 13533.04 -2342.04 6 11391 13533.04 -2142.04 7 11793 13533.04 -1740.04 8 13933 13533.04 399.96 9 12778 13533.04 -755.04 10 11810 13533.04 -1723.04 11 13698 13533.04 164.960000000000 12 11956 13533.04 -1577.04 13 10723 13533.04 -2810.04 14 13938 13533.04 404.96 15 13979 13533.04 445.96 16 13807 13533.04 273.96 17 12973 13533.04 -560.04 18 12509 13533.04 -1024.04 19 12934 13533.04 -599.04 20 14908 13533.04 1374.96 21 13772 13533.04 238.960000000000 22 13012 13533.04 -521.04 23 14049 13533.04 515.96 24 11816 13533.04 -1717.04 25 11593 13533.04 -1940.04 26 14466 13533.04 932.96 27 13615 13533.04 81.9600000000003 28 14733 13533.04 1199.96 29 13880 13533.04 346.96 30 13527 13533.04 -6.03999999999974 31 13584 13533.04 50.9600000000003 32 16170 13533.04 2636.96 33 13260 13533.04 -273.04 34 14741 13533.04 1207.96 35 15486 13533.04 1952.96 36 13154 13533.04 -379.04 37 12621 13533.04 -912.04 38 15031 13533.04 1497.96 39 15452 13533.04 1918.96 40 15428 13533.04 1894.96 41 13105 13533.04 -428.04 42 14716 13533.04 1182.96 43 14180 13533.04 646.96 44 16202 13533.04 2668.96 45 14392 13533.04 858.96 46 15140 13533.04 1606.96 47 15960 13533.04 2426.96 48 14351 13533.04 817.96 49 13230 13533.04 -303.04 50 15202 13533.04 1668.96 51 17157 16905.7 251.3 52 16159 16905.7 -746.7 53 13405 16905.7 -3500.7 54 17224 16905.7 318.3 55 17338 16905.7 432.3 56 17370 16905.7 464.3 57 18817 16905.7 1911.3 58 16593 16905.7 -312.7 59 17979 16905.7 1073.3 60 17015 16905.7 109.3 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.833211780427027 0.333576439145947 0.166788219572973 6 0.74503931369706 0.50992137260588 0.25496068630294 7 0.648509533506368 0.702980932987264 0.351490466493632 8 0.77116743862044 0.457665122759120 0.228832561379560 9 0.713159798162836 0.573680403674329 0.286840201837164 10 0.648487842561724 0.703024314876552 0.351512157438276 11 0.670320269967883 0.659359460064234 0.329679730032117 12 0.61413999038455 0.7717200192309 0.38586000961545 13 0.711754513948102 0.576490972103797 0.288245486051898 14 0.754221117425685 0.491557765148629 0.245778882574315 15 0.775144517044905 0.44971096591019 0.224855482955095 16 0.767618617095783 0.464762765808435 0.232381382904217 17 0.723432789678796 0.553134420642408 0.276567210321204 18 0.686316020573067 0.627367958853866 0.313683979426933 19 0.641988686479182 0.716022627041637 0.358011313520818 20 0.73504940689727 0.52990118620546 0.26495059310273 21 0.703396562865846 0.593206874268309 0.296603437134154 22 0.658959938632154 0.682080122735692 0.341040061367846 23 0.634704393055439 0.730591213889123 0.365295606944561 24 0.686810959696512 0.626378080606976 0.313189040303488 25 0.786497595532322 0.427004808935356 0.213502404467678 26 0.789944644370933 0.420110711258135 0.210055355629067 27 0.760924488456597 0.478151023086807 0.239075511543403 28 0.770498235870744 0.459003528258513 0.229501764129256 29 0.737006130353664 0.525987739292672 0.262993869646336 30 0.702641554974501 0.594716890050999 0.297358445025499 31 0.667335282128038 0.665329435743923 0.332664717871962 32 0.814242678405339 0.371514643189323 0.185757321594661 33 0.79463300344461 0.410733993110779 0.205366996555390 34 0.773438467385724 0.453123065228551 0.226561532614276 35 0.797002323536671 0.405995352926658 0.202997676463329 36 0.783423795719216 0.433152408561567 0.216576204280783 37 0.826648464140338 0.346703071719324 0.173351535859662 38 0.806405424485875 0.38718915102825 0.193594575514125 39 0.805369653324694 0.389260693350612 0.194630346675306 40 0.798485831823424 0.403028336353151 0.201514168176576 41 0.80354082913346 0.392918341733078 0.196459170866539 42 0.75607908237957 0.487841835240861 0.243920917620431 43 0.7043415534951 0.591316893009801 0.295658446504900 44 0.751910408140668 0.496179183718665 0.248089591859332 45 0.685198936435753 0.629602127128494 0.314801063564247 46 0.626751693583784 0.746496612832433 0.373248306416216 47 0.657543061955817 0.684913876088366 0.342456938044183 48 0.566030108749218 0.867939782501565 0.433969891250782 49 0.538633645567238 0.922732708865523 0.461366354432762 50 0.448742334232807 0.897484668465615 0.551257665767193 51 0.341767987569123 0.683535975138245 0.658232012430877 52 0.260312987015315 0.520625974030631 0.739687012984685 53 0.926008144160547 0.147983711678907 0.0739918558394534 54 0.854201497269384 0.291597005461232 0.145798502730616 55 0.723965280364052 0.552069439271896 0.276034719635948 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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