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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 05:36:10 -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/t1227789497y26tib3099p5kqp.htm/, Retrieved Thu, 27 Nov 2008 12:38:17 +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/t1227789497y26tib3099p5kqp.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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Dataseries X:

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105.4 109.1 107.1 111.4 110.7 114.1 117.1 121.8 118.7 127.6 126.5 129.9 127.5 128 134.6 123.5 131.8 124 135.9 127.4 142.7 127.6 141.7 128.4 153.4 131.4 145 135.1 137.7 134 148.3 144.5 152.2 147.3 169.4 150.9 168.6 148.7 161.1 141.4 174.1 138.9 179 139.8 190.6 145.6 190 147.9 181.6 148.5 174.8 151.1 180.5 157.5 196.8 167.5 193.8 172.3 197 173.5 216.3 187.5 221.4 205.5 217.9 195.1 229.7 204.5 227.4 204.5 204.2 201.7 196.6 207 198.8 206.6 207.5 210.6 190.7 211.1 201.6 215 210.5 223.9 223.5 238.2 223.8 238.9 231.2 229.6 244 232.2 234.7 222.1 250.2 221.6 265.7 227.3 287.6 221 283.3 213.6 295.4 243.4 312.3 253.8 333.8 265.3 347.7 268.2 383.2 268.5 407.1 266.9 413.6 268.4 362.7 250.8 321.9 231.2 239.4 192

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation alg_indexcijfer_grondstoffen[t] = + 28.6031604240415 + 0.613848589128495indexcijfer_industr_grondstoffen[t] -9.91563842933872M1[t] -4.10807717988457M2[t] -5.57956194365494M3[t] -9.2283344982305M4[t] -8.75579974377452M5[t] -2.59871104575340M6[t] + 1.16748553939799M7[t] + 6.1967995092808M8[t] + 14.4705898728474M9[t] + 18.1185448337778M10[t] + 9.77590364882332M11[t] + 2.18674406177216t + 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) 28.6031604240415 32.957818 0.8679 0.389874 0.194937 indexcijfer_industr_grondstoffen 0.613848589128495 0.313135 1.9603 0.0559 0.02795 M1 -9.91563842933872 19.149104 -0.5178 0.607018 0.303509 M2 -4.10807717988457 20.127389 -0.2041 0.839154 0.419577 M3 -5.57956194365494 20.065291 -0.2781 0.782178 0.391089 M4 -9.2283344982305 20.396 -0.4525 0.653021 0.32651 M5 -8.75579974377452 20.571324 -0.4256 0.672319 0.33616 M6 -2.59871104575340 20.784164 -0.125 0.901031 0.450515 M7 1.16748553939799 21.027833 0.0555 0.955959 0.477979 M8 6.1967995092808 20.901497 0.2965 0.768173 0.384086 M9 14.4705898728474 20.327071 0.7119 0.480053 0.240027 M10 18.1185448337778 20.378865 0.8891 0.378485 0.189243 M11 9.77590364882332 20.033634 0.488 0.627837 0.313918 t 2.18674406177216 0.857108 2.5513 0.014046 0.007023 Multiple Linear Regression - Regression Statistics Multiple R 0.928902481768124 R-squared 0.86285982063498 Adjusted R-squared 0.824927430597848 F-TEST (value) 22.7473096156162 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 5.55111512312578e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 31.5050895272108 Sum Squared Residuals 46650.8213075257 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.4 87.8451471303938 17.5548528696062 2 107.1 97.2513041966157 9.84869580338425 3 110.7 99.6239546852644 11.0760453147356 4 117.1 102.888560328750 14.2114396712496 5 118.7 109.108160961924 9.5918390380762 6 126.5 118.863845476713 7.63615452328737 7 127.5 123.650473804292 3.84952619570795 8 134.6 128.104213184869 6.49578681513122 9 131.8 138.871671904772 -7.07167190477182 10 135.9 146.793456130511 -10.8934561305113 11 142.7 140.760328725155 1.93967127484537 12 141.7 133.662248009406 8.03775199059373 13 153.4 127.774899409225 25.6251005907748 14 145 138.040444500227 6.95955549977308 15 137.7 138.080470350187 -0.380470350187385 16 148.3 143.063852043233 5.23614795676683 17 152.2 147.441906909021 4.75809309097889 18 169.4 157.995594589677 11.4044054103230 19 168.6 162.598068340518 6.00193165948218 20 161.1 165.333031671535 -4.23303167153478 21 174.1 174.258944624052 -0.158944624052340 22 179 180.646107376971 -1.64610737697053 23 190.6 178.050532070733 12.5494679292665 24 190 171.873224238678 18.1267757613222 25 181.6 164.512639024588 17.0873609754116 26 174.8 174.102950667549 0.69704933245124 27 180.5 178.746840935973 1.75315906402706 28 196.8 183.423298334454 13.3767016655455 29 193.8 189.029050378499 4.7709496215006 30 197 198.109501445247 -1.10950144524688 31 216.3 212.656322339969 3.64367766003065 32 221.4 230.921654975937 -9.52165497593724 33 217.9 234.998164074340 -17.0981640743397 34 229.7 246.60303983485 -16.9030398348501 35 227.4 240.447142711668 -13.0471427116677 36 204.2 231.139207075057 -26.9392070750568 37 196.6 226.663710229871 -30.0637102298713 38 198.8 234.412476105446 -35.6124761054462 39 207.5 237.583129759962 -30.0831297599620 40 190.7 236.428025561723 -45.7280255617228 41 201.6 241.481313875552 -39.8813138755521 42 210.5 255.288399078589 -44.7883990785889 43 223.5 270.01937455005 -46.51937455005 44 223.8 277.665126594095 -53.8651265940949 45 231.2 282.416869140539 -51.2168691405387 46 244 289.847574494975 -45.8475744949753 47 234.7 277.491806621595 -42.7918066215952 48 250.2 269.59572273998 -19.3957227399798 49 265.7 265.365765330446 0.334234669554334 50 287.6 269.492824530162 18.1071754698376 51 283.3 265.665604268613 17.6343957313867 52 295.4 282.496263731839 12.9037362681609 53 312.3 291.539567875004 20.7604321249964 54 333.8 306.942659409775 26.8573405902254 55 347.7 314.675760965171 33.0242390348292 56 383.2 322.075973573564 61.1240264264357 57 407.1 331.554350256297 75.5456497437025 58 413.6 338.309822162693 75.2901778373072 59 362.7 321.350189870849 41.3498101291510 60 321.9 301.729597936879 20.1704020631207 61 239.4 269.937838875476 -30.5378388754757 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0051907692313537 0.0103815384627074 0.994809230768646 18 0.00114226087219828 0.00228452174439656 0.998857739127802 19 0.000190624948041361 0.000381249896082722 0.999809375051959 20 2.70235227881552e-05 5.40470455763104e-05 0.999972976477212 21 1.19124389000211e-05 2.38248778000421e-05 0.9999880875611 22 2.08652895471236e-06 4.17305790942473e-06 0.999997913471045 23 6.19333239308848e-07 1.23866647861770e-06 0.99999938066676 24 2.11642467713562e-07 4.23284935427124e-07 0.999999788357532 25 7.29114405679078e-08 1.45822881135816e-07 0.99999992708856 26 2.30454429736844e-08 4.60908859473688e-08 0.999999976954557 27 3.9747525883582e-09 7.9495051767164e-09 0.999999996025247 28 1.98450848333520e-09 3.96901696667041e-09 0.999999998015492 29 5.46777540508333e-10 1.09355508101667e-09 0.999999999453222 30 4.54001606226605e-10 9.0800321245321e-10 0.999999999545998 31 9.78292855875066e-10 1.95658571175013e-09 0.999999999021707 32 6.63917070037311e-10 1.32783414007462e-09 0.999999999336083 33 9.0249954260305e-10 1.8049990852061e-09 0.9999999990975 34 1.79012231676239e-09 3.58024463352479e-09 0.999999998209878 35 5.12076498740364e-08 1.02415299748073e-07 0.99999994879235 36 4.70582224234419e-05 9.41164448468838e-05 0.999952941777577 37 0.00215702619865259 0.00431405239730518 0.997842973801347 38 0.00227377062257020 0.00454754124514040 0.99772622937743 39 0.00129752796803352 0.00259505593606704 0.998702472031966 40 0.0107702261985997 0.0215404523971993 0.9892297738014 41 0.0568942882266499 0.113788576453300 0.94310571177335 42 0.391970423481614 0.783940846963228 0.608029576518386 43 0.461579194722659 0.923158389445317 0.538420805277341 44 0.428937475195673 0.857874950391347 0.571062524804327 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.785714285714286 NOK 5% type I error level 24 0.857142857142857 NOK 10% type I error level 24 0.857142857142857 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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