WS7 Multiple Regression Analysis

*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: Fri, 20 Nov 2009 12:53:18 -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/20/t1258746849czfail3nrmoihap.htm/, Retrieved Fri, 20 Nov 2009 20:54:21 +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/20/t1258746849czfail3nrmoihap.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:

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2.7 0 2.3 0 1.9 0 2.0 0 2.3 0 2.8 0 2.4 0 2.3 0 2.7 0 2.7 0 2.9 0 3.0 0 2.2 0 2.3 0 2.8 0 2.8 0 2.8 0 2.2 0 2.6 0 2.8 0 2.5 0 2.4 0 2.3 0 1.9 0 1.7 0 2.0 0 2.1 0 1.7 0 1.8 0 1.8 0 1.8 0 1.3 0 1.3 0 1.3 1 1.2 1 1.4 1 2.2 1 2.9 1 3.1 1 3.5 1 3.6 1 4.4 1 4.1 1 5.1 1 5.8 1 5.9 1 5.4 1 5.5 1 4.8 1 3.2 1 2.7 1 2.1 1 1.9 1 0.6 1 0.7 1 -0.2 1 -1.0 1 -1.7 1 -0.7 1 -1.0 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Inflatie[t] = + 2.0125 + 0.245833333333334Kredietcrisis[t] + 0.609166666666665M1[t] + 0.429166666666667M2[t] + 0.409166666666666M3[t] + 0.309166666666666M4[t] + 0.369166666666667M5[t] + 0.249166666666667M6[t] + 0.209166666666666M7[t] + 0.149166666666667M8[t] + 0.149166666666667M9[t] -0.0400000000000002M10[t] + 0.0600000000000002M11[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) 2.0125 0.811399 2.4803 0.016766 0.008383 Kredietcrisis 0.245833333333334 0.450777 0.5454 0.588089 0.294044 M1 0.609166666666665 1.085615 0.5611 0.577377 0.288689 M2 0.429166666666667 1.085615 0.3953 0.694394 0.347197 M3 0.409166666666666 1.085615 0.3769 0.707945 0.353973 M4 0.309166666666666 1.085615 0.2848 0.77706 0.38853 M5 0.369166666666667 1.085615 0.3401 0.735332 0.367666 M6 0.249166666666667 1.085615 0.2295 0.819463 0.409732 M7 0.209166666666666 1.085615 0.1927 0.848047 0.424023 M8 0.149166666666667 1.085615 0.1374 0.891299 0.44565 M9 0.149166666666667 1.085615 0.1374 0.891299 0.44565 M10 -0.0400000000000002 1.081865 -0.037 0.970663 0.485331 M11 0.0600000000000002 1.081865 0.0555 0.956007 0.478004 Multiple Linear Regression - Regression Statistics Multiple R 0.135977832184842 R-squared 0.0184899708456891 Adjusted R-squared -0.232108334470305 F-TEST (value) 0.0737833036116267 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.99998817080419 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.71057878720451 Sum Squared Residuals 137.52575 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.7 2.62166666666668 0.0783333333333253 2 2.3 2.44166666666667 -0.141666666666665 3 1.9 2.42166666666667 -0.521666666666667 4 2 2.32166666666667 -0.321666666666667 5 2.3 2.38166666666667 -0.0816666666666665 6 2.8 2.26166666666667 0.538333333333332 7 2.4 2.22166666666667 0.178333333333334 8 2.3 2.16166666666667 0.138333333333334 9 2.7 2.16166666666667 0.538333333333334 10 2.7 1.9725 0.7275 11 2.9 2.0725 0.8275 12 3 2.0125 0.9875 13 2.2 2.62166666666666 -0.421666666666664 14 2.3 2.44166666666667 -0.141666666666667 15 2.8 2.42166666666667 0.378333333333334 16 2.8 2.32166666666667 0.478333333333334 17 2.8 2.38166666666667 0.418333333333333 18 2.2 2.26166666666667 -0.0616666666666665 19 2.6 2.22166666666667 0.378333333333334 20 2.8 2.16166666666667 0.638333333333334 21 2.5 2.16166666666667 0.338333333333333 22 2.4 1.9725 0.4275 23 2.3 2.0725 0.2275 24 1.9 2.0125 -0.112500000000000 25 1.7 2.62166666666666 -0.921666666666665 26 2 2.44166666666667 -0.441666666666666 27 2.1 2.42166666666667 -0.321666666666666 28 1.7 2.32166666666667 -0.621666666666666 29 1.8 2.38166666666667 -0.581666666666667 30 1.8 2.26166666666667 -0.461666666666667 31 1.8 2.22166666666667 -0.421666666666666 32 1.3 2.16166666666667 -0.861666666666666 33 1.3 2.16166666666667 -0.861666666666666 34 1.3 2.21833333333333 -0.918333333333333 35 1.2 2.31833333333333 -1.11833333333333 36 1.4 2.25833333333333 -0.858333333333334 37 2.2 2.8675 -0.667499999999999 38 2.9 2.6875 0.212499999999999 39 3.1 2.6675 0.4325 40 3.5 2.5675 0.9325 41 3.6 2.6275 0.9725 42 4.4 2.5075 1.8925 43 4.1 2.4675 1.6325 44 5.1 2.4075 2.6925 45 5.8 2.4075 3.3925 46 5.9 2.21833333333333 3.68166666666667 47 5.4 2.31833333333333 3.08166666666667 48 5.5 2.25833333333333 3.24166666666667 49 4.8 2.8675 1.9325 50 3.2 2.6875 0.5125 51 2.7 2.6675 0.0324999999999999 52 2.1 2.5675 -0.4675 53 1.9 2.6275 -0.7275 54 0.6 2.5075 -1.9075 55 0.7 2.4675 -1.7675 56 -0.2 2.4075 -2.6075 57 -1 2.4075 -3.4075 58 -1.7 2.21833333333333 -3.91833333333333 59 -0.7 2.31833333333333 -3.01833333333333 60 -1 2.25833333333333 -3.25833333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0226415726796944 0.0452831453593887 0.977358427320306 17 0.0060149318278533 0.0120298636557066 0.993985068172147 18 0.00175519370730880 0.00351038741461759 0.998244806292691 19 0.000355728675883654 0.000711457351767308 0.999644271324116 20 9.05990640179736e-05 0.000181198128035947 0.999909400935982 21 1.68246979634576e-05 3.36493959269153e-05 0.999983175302037 22 3.2745470708898e-06 6.5490941417796e-06 0.99999672545293 23 9.5311937907942e-07 1.90623875815884e-06 0.99999904688062 24 8.63235589500881e-07 1.72647117900176e-06 0.99999913676441 25 3.76601293769095e-07 7.5320258753819e-07 0.999999623398706 26 7.55785418836321e-08 1.51157083767264e-07 0.999999924421458 27 1.39007506214718e-08 2.78015012429437e-08 0.99999998609925 28 5.06519650858046e-09 1.01303930171609e-08 0.999999994934804 29 1.97935364450268e-09 3.95870728900535e-09 0.999999998020646 30 6.64282338176126e-10 1.32856467635225e-09 0.999999999335718 31 2.16073587231963e-10 4.32147174463926e-10 0.999999999783926 32 2.65471738856274e-10 5.30943477712549e-10 0.999999999734528 33 2.83961175764543e-10 5.67922351529086e-10 0.999999999716039 34 4.91950460330059e-11 9.83900920660118e-11 0.999999999950805 35 8.4312701722867e-12 1.68625403445734e-11 0.999999999991569 36 1.37822415580796e-12 2.75644831161593e-12 0.999999999998622 37 1.06211244349010e-12 2.12422488698021e-12 0.999999999998938 38 1.39085626708724e-12 2.78171253417449e-12 0.99999999999861 39 9.34200461682138e-13 1.86840092336428e-12 0.999999999999066 40 1.04186579472700e-12 2.08373158945401e-12 0.999999999998958 41 5.80743126466267e-13 1.16148625293253e-12 0.99999999999942 42 1.96106266934760e-12 3.92212533869521e-12 0.99999999999804 43 1.62127461758339e-12 3.24254923516679e-12 0.999999999998379 44 1.97462267047088e-11 3.94924534094176e-11 0.999999999980254 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.93103448275862 NOK 5% type I error level 29 1 NOK 10% type I error level 29 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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