Multiple Linear Regression Prijsindexcijfers Grondstoffen

*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: Mon, 24 Nov 2008 03:34:53 -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/t12275229864srp2b9usypewzo.htm/, Retrieved Mon, 24 Nov 2008 10:36:26 +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/t12275229864srp2b9usypewzo.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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101 0 104 0 99 0 105 0 107 0 111 0 117 0 119 0 127 0 128 0 135 0 132 0 136 0 143 0 142 0 153 0 145 0 138 0 148 0 152 0 169 0 169 0 161 0 174 0 179 0 191 0 190 0 182 0 175 0 181 0 197 0 194 0 197 0 216 0 221 0 218 0 230 0 227 0 204 0 197 0 199 0 208 0 191 0 202 0 211 0 224 1 224 1 231 1 244 1 235 1 250 1 266 1 288 1 283 1 295 1 312 1 334 1 348 1 383 1 407 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation IGrSt[t] = + 108.518518518518 + 25.7037037037037D[t] -14.5481481481482M1[t] -15.7037037037037M2[t] -21.8592592592593M3[t] -21.4148148148148M4[t] -22.3703703703704M5[t] -24.1259259259259M6[t] -21.8814814814815M7[t] -18.8370370370370M8[t] -10.1925925925926M9[t] -9.0888888888889M10[t] -4.44444444444445M11[t] + 3.15555555555556t + 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) 108.518518518518 14.201292 7.6415 0 0 D 25.7037037037037 12.110903 2.1224 0.039223 0.019611 M1 -14.5481481481482 16.79501 -0.8662 0.390866 0.195433 M2 -15.7037037037037 16.77043 -0.9364 0.353961 0.176981 M3 -21.8592592592593 16.751287 -1.3049 0.198407 0.099204 M4 -21.4148148148148 16.7376 -1.2794 0.207157 0.103578 M5 -22.3703703703704 16.729383 -1.3372 0.187736 0.093868 M6 -24.1259259259259 16.726643 -1.4424 0.155974 0.077987 M7 -21.8814814814815 16.729383 -1.308 0.197383 0.098692 M8 -18.8370370370370 16.7376 -1.1254 0.266244 0.133122 M9 -10.1925925925926 16.751287 -0.6085 0.545871 0.272936 M10 -9.0888888888889 16.660746 -0.5455 0.588027 0.294013 M11 -4.44444444444445 16.652491 -0.2669 0.790744 0.395372 t 3.15555555555556 0.302773 10.4222 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.942402549209953 R-squared 0.888122564757418 Adjusted R-squared 0.856505028710601 F-TEST (value) 28.0895564867027 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 26.3255476780162 Sum Squared Residuals 31879.5851851852 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101 97.125925925926 3.87407407407398 2 104 99.125925925926 4.87407407407406 3 99 96.125925925926 2.87407407407408 4 105 99.725925925926 5.27407407407407 5 107 101.925925925926 5.07407407407408 6 111 103.325925925926 7.67407407407407 7 117 108.725925925926 8.27407407407408 8 119 114.925925925926 4.07407407407408 9 127 126.725925925926 0.274074074074094 10 128 130.985185185185 -2.98518518518516 11 135 138.785185185185 -3.78518518518518 12 132 146.385185185185 -14.3851851851852 13 136 134.992592592593 1.00740740740743 14 143 136.992592592593 6.00740740740739 15 142 133.992592592593 8.00740740740741 16 153 137.592592592593 15.4074074074074 17 145 139.792592592593 5.20740740740741 18 138 141.192592592593 -3.19259259259259 19 148 146.592592592593 1.4074074074074 20 152 152.792592592593 -0.792592592592592 21 169 164.592592592593 4.40740740740742 22 169 168.851851851852 0.148148148148156 23 161 176.651851851852 -15.6518518518518 24 174 184.251851851852 -10.2518518518518 25 179 172.859259259259 6.14074074074078 26 191 174.859259259259 16.1407407407408 27 190 171.859259259259 18.1407407407407 28 182 175.459259259259 6.54074074074075 29 175 177.659259259259 -2.65925925925927 30 181 179.059259259259 1.94074074074075 31 197 184.459259259259 12.5407407407407 32 194 190.659259259259 3.34074074074075 33 197 202.459259259259 -5.45925925925927 34 216 206.718518518519 9.28148148148146 35 221 214.518518518519 6.48148148148148 36 218 222.118518518519 -4.11851851851852 37 230 210.725925925926 19.2740740740741 38 227 212.725925925926 14.2740740740741 39 204 209.725925925926 -5.72592592592594 40 197 213.325925925926 -16.3259259259259 41 199 215.525925925926 -16.5259259259259 42 208 216.925925925926 -8.92592592592594 43 191 222.325925925926 -31.3259259259259 44 202 228.525925925926 -26.5259259259259 45 211 240.325925925926 -29.3259259259259 46 224 270.288888888889 -46.2888888888889 47 224 278.088888888889 -54.0888888888889 48 231 285.688888888889 -54.6888888888889 49 244 274.296296296296 -30.2962962962963 50 235 276.296296296296 -41.2962962962963 51 250 273.296296296296 -23.2962962962963 52 266 276.896296296296 -10.8962962962963 53 288 279.096296296296 8.9037037037037 54 283 280.496296296296 2.50370370370371 55 295 285.896296296296 9.1037037037037 56 312 292.096296296296 19.9037037037037 57 334 303.896296296296 30.1037037037037 58 348 308.155555555556 39.8444444444444 59 383 315.955555555556 67.0444444444444 60 407 323.555555555556 83.4444444444444 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00293286268715088 0.00586572537430177 0.99706713731285 18 0.00185142752471892 0.00370285504943783 0.998148572475281 19 0.000406239189281596 0.000812478378563191 0.999593760810718 20 6.81641755978409e-05 0.000136328351195682 0.999931835824402 21 1.23972283470065e-05 2.47944566940130e-05 0.999987602771653 22 1.85848864241253e-06 3.71697728482507e-06 0.999998141511358 23 8.50222513540588e-07 1.70044502708118e-06 0.999999149777486 24 1.44563825867371e-07 2.89127651734743e-07 0.999999855436174 25 2.53708046438792e-08 5.07416092877585e-08 0.999999974629195 26 1.50906004864213e-08 3.01812009728425e-08 0.9999999849094 27 1.04509110814302e-08 2.09018221628603e-08 0.999999989549089 28 3.45193704083778e-09 6.90387408167555e-09 0.999999996548063 29 1.54977717250219e-09 3.09955434500437e-09 0.999999998450223 30 3.3390928901994e-10 6.6781857803988e-10 0.99999999966609 31 2.59535513808233e-10 5.19071027616466e-10 0.999999999740464 32 1.60073416389761e-10 3.20146832779521e-10 0.999999999839927 33 4.94356937256122e-10 9.88713874512244e-10 0.999999999505643 34 9.82041151411343e-10 1.96408230282269e-09 0.999999999017959 35 5.65201113617721e-09 1.13040222723544e-08 0.999999994347989 36 5.54657854016118e-09 1.10931570803224e-08 0.999999994453421 37 4.94931185021643e-08 9.89862370043285e-08 0.999999950506882 38 6.52651032239021e-06 1.30530206447804e-05 0.999993473489678 39 0.000625494078259349 0.00125098815651870 0.99937450592174 40 0.0114400084685712 0.0228800169371424 0.988559991531429 41 0.0136447185991305 0.027289437198261 0.98635528140087 42 0.0526337565808943 0.105267513161789 0.947366243419106 43 0.0932141425003816 0.186428285000763 0.906785857499618 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 23 0.851851851851852 NOK 5% type I error level 25 0.925925925925926 NOK 10% type I error level 25 0.925925925925926 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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