*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: Thu, 19 Nov 2009 00:57:27 -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/Nov/19/t1258618150mlcqf20cubxuwro.htm/, Retrieved Thu, 19 Nov 2009 09:09:22 +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/Nov/19/t1258618150mlcqf20cubxuwro.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:

» Textbox « » Textfile « » CSV «

3353 1 3186 1 3902 1 4164 1 3499 1 4145 1 3796 1 3711 1 3949 1 3740 1 3243 1 4407 1 4814 1 3908 1 5250 1 3937 1 4004 1 5560 1 3922 1 3759 1 4138 1 4634 1 3996 1 4308 1 4143 0 4429 0 5219 0 4929 0 5755 0 5592 0 4163 0 4962 0 5208 0 4755 0 4491 0 5732 0 5731 0 5040 0 6102 0 4904 0 5369 0 5578 0 4619 0 4731 0 5011 0 5299 0 4146 0 4625 0 4736 0 4219 0 5116 0 4205 0 4121 0 5103 1 4300 1 4578 1 3809 1 5526 1 4247 1 3830 1 4394 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] = + 4928.62068965517 -768.870689655172X[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) 4928.62068965517 108.116905 45.586 0 0 X -768.870689655172 149.273782 -5.1507 3e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.556942268030847 R-squared 0.310184689919343 Adjusted R-squared 0.298492905002722 F-TEST (value) 26.5301399342694 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 3.13940417195901e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 582.227354212241 Sum Squared Residuals 20000332.8275862 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3353 4159.74999999999 -806.74999999999 2 3186 4159.75 -973.75 3 3902 4159.75 -257.750000000000 4 4164 4159.75 4.24999999999969 5 3499 4159.75 -660.75 6 4145 4159.75 -14.7500000000003 7 3796 4159.75 -363.750 8 3711 4159.75 -448.75 9 3949 4159.75 -210.750000000000 10 3740 4159.75 -419.75 11 3243 4159.75 -916.75 12 4407 4159.75 247.250000000000 13 4814 4159.75 654.25 14 3908 4159.75 -251.750000000000 15 5250 4159.75 1090.25 16 3937 4159.75 -222.750000000000 17 4004 4159.75 -155.750000000000 18 5560 4159.75 1400.25 19 3922 4159.75 -237.750000000000 20 3759 4159.75 -400.750000000000 21 4138 4159.75 -21.7500000000003 22 4634 4159.75 474.25 23 3996 4159.75 -163.750000000000 24 4308 4159.75 148.250000000000 25 4143 4928.62068965517 -785.620689655173 26 4429 4928.62068965517 -499.620689655173 27 5219 4928.62068965517 290.379310344827 28 4929 4928.62068965517 0.379310344827474 29 5755 4928.62068965517 826.379310344827 30 5592 4928.62068965517 663.379310344827 31 4163 4928.62068965517 -765.620689655173 32 4962 4928.62068965517 33.3793103448275 33 5208 4928.62068965517 279.379310344827 34 4755 4928.62068965517 -173.620689655173 35 4491 4928.62068965517 -437.620689655173 36 5732 4928.62068965517 803.379310344827 37 5731 4928.62068965517 802.379310344827 38 5040 4928.62068965517 111.379310344827 39 6102 4928.62068965517 1173.37931034483 40 4904 4928.62068965517 -24.6206896551725 41 5369 4928.62068965517 440.379310344827 42 5578 4928.62068965517 649.379310344827 43 4619 4928.62068965517 -309.620689655173 44 4731 4928.62068965517 -197.620689655173 45 5011 4928.62068965517 82.3793103448275 46 5299 4928.62068965517 370.379310344827 47 4146 4928.62068965517 -782.620689655173 48 4625 4928.62068965517 -303.620689655173 49 4736 4928.62068965517 -192.620689655173 50 4219 4928.62068965517 -709.620689655173 51 5116 4928.62068965517 187.379310344827 52 4205 4928.62068965517 -723.620689655173 53 4121 4928.62068965517 -807.620689655173 54 5103 4159.75 943.25 55 4300 4159.75 140.250000000000 56 4578 4159.75 418.25 57 3809 4159.75 -350.750 58 5526 4159.75 1366.25 59 4247 4159.75 87.2499999999997 60 3830 4159.75 -329.750000000000 61 4394 4159.75 234.250000000000 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.421828447741818 0.843656895483635 0.578171552258183 6 0.37813358148766 0.75626716297532 0.62186641851234 7 0.247139681482926 0.494279362965852 0.752860318517074 8 0.152425245059442 0.304850490118884 0.847574754940558 9 0.0983547024715162 0.196709404943032 0.901645297528484 10 0.0562718849000152 0.112543769800030 0.943728115099985 11 0.0738230108440166 0.147646021688033 0.926176989155983 12 0.117645058980574 0.235290117961148 0.882354941019426 13 0.299296052670174 0.598592105340347 0.700703947329826 14 0.22943053134549 0.45886106269098 0.77056946865451 15 0.599353150081758 0.801293699836484 0.400646849918242 16 0.522762032332511 0.954475935334978 0.477237967667489 17 0.445824412716702 0.891648825433405 0.554175587283298 18 0.832193657426404 0.335612685147191 0.167806342573595 19 0.787162031927546 0.425675936144908 0.212837968072454 20 0.757594853959264 0.484810292081471 0.242405146040736 21 0.698371866118307 0.603256267763387 0.301628133881693 22 0.676541589399226 0.646916821201549 0.323458410600774 23 0.619353665090258 0.761292669819484 0.380646334909742 24 0.554288052245527 0.891423895508946 0.445711947754473 25 0.53625750045066 0.92748499909868 0.46374249954934 26 0.493034001465934 0.986068002931868 0.506965998534066 27 0.499902876935601 0.999805753871202 0.500097123064399 28 0.434634734755262 0.869269469510524 0.565365265244738 29 0.537510447643594 0.924979104712812 0.462489552356406 30 0.556767381129516 0.886465237740967 0.443232618870484 31 0.612982356985027 0.774035286029947 0.387017643014973 32 0.539074779256421 0.921850441487158 0.460925220743579 33 0.480943901957897 0.961887803915794 0.519056098042103 34 0.412120088013933 0.824240176027865 0.587879911986067 35 0.378969957582511 0.757939915165021 0.62103004241749 36 0.445967976130153 0.891935952260306 0.554032023869847 37 0.517111744070765 0.96577651185847 0.482888255929235 38 0.443838866542169 0.887677733084339 0.556161133457831 39 0.713472830632957 0.573054338734085 0.286527169367043 40 0.646513937079051 0.706972125841897 0.353486062920949 41 0.647374595233811 0.705250809532378 0.352625404766189 42 0.74019508014795 0.5196098397041 0.25980491985205 43 0.680903793953448 0.638192412093103 0.319096206046552 44 0.61048152273178 0.779036954536439 0.389518477268219 45 0.563790518840561 0.872418962318877 0.436209481159439 46 0.624835140441168 0.750329719117664 0.375164859558832 47 0.610064478898808 0.779871042202385 0.389935521101192 48 0.528614140740483 0.942771718519033 0.471385859259517 49 0.4546494880671 0.9092989761342 0.5453505119329 50 0.397835388384377 0.795670776768754 0.602164611615623 51 0.455385576688414 0.910771153376827 0.544614423311586 52 0.371569821029175 0.743139642058349 0.628430178970825 53 0.289084582819584 0.578169165639168 0.710915417180416 54 0.327605504484744 0.655211008969488 0.672394495515256 55 0.214073034495084 0.428146068990168 0.785926965504916 56 0.12792019280355 0.2558403856071 0.87207980719645 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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