loiqueverhasselt

*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: Sun, 23 Nov 2008 13:12:15 -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/23/t1227471228jx2php97kz8tifg.htm/, Retrieved Sun, 23 Nov 2008 20:13:57 +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/23/t1227471228jx2php97kz8tifg.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Seatbelt Q3 2

Dataseries X:

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99.4 0 97.5 0 94.6 0 92.6 0 92.5 0 89.8 0 88.8 0 87.4 0 85.2 0 83.1 0 84.7 0 84.8 0 85.8 0 86.3 0 89 0 89 0 89.3 0 91.9 0 94.9 0 94.4 0 96.8 0 96.9 0 98 0 97.9 0 100.9 0 103.9 0 103.1 0 102.5 0 104.3 0 102.6 0 101.7 0 102.8 0 105.4 0 110.9 1 113.5 1 116.3 1 124 1 128.8 1 133.5 1 132.6 1 128.4 1 127.3 1 126.7 1 123.3 1 123.2 1 124.4 1 128.2 1 128.7 1 135.7 1 139 1 145.4 1 142.4 1 137.7 1 137 1 137.1 1 139.3 1 139.6 1 140.4 1 142.3 1 148.3 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 Grondstofprijzen[t] = + 79.3416666666667 + 16.0138888888889Wet[t] + 5.18361111111106M1[t] + 6.39444444444447M2[t] + 7.68527777777776M3[t] + 5.6561111111111M4[t] + 3.54694444444444M5[t] + 2.09777777777777M6[t] + 1.48861111111111M7[t] + 0.359444444444446M8[t] + 0.230277777777773M9[t] -2.60166666666667M10[t] -1.13083333333334M11[t] + 0.729166666666667t + 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) 79.3416666666667 2.825276 28.0828 0 0 Wet 16.0138888888889 2.718623 5.8904 0 0 M1 5.18361111111106 3.29709 1.5722 0.122763 0.061382 M2 6.39444444444447 3.288673 1.9444 0.057979 0.028989 M3 7.68527777777776 3.282112 2.3416 0.02359 0.011795 M4 5.6561111111111 3.277417 1.7258 0.091099 0.045549 M5 3.54694444444444 3.274597 1.0832 0.284378 0.142189 M6 2.09777777777777 3.273656 0.6408 0.524829 0.262414 M7 1.48861111111111 3.274597 0.4546 0.65154 0.32577 M8 0.359444444444446 3.277417 0.1097 0.913146 0.456573 M9 0.230277777777773 3.282112 0.0702 0.944369 0.472185 M10 -2.60166666666667 3.266122 -0.7966 0.429798 0.214899 M11 -1.13083333333334 3.263292 -0.3465 0.730524 0.365262 t 0.729166666666667 0.07848 9.2911 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.974578140622656 R-squared 0.949802552179514 Adjusted R-squared 0.935616316925898 F-TEST (value) 66.9524038759638 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.15822522187752 Sum Squared Residuals 1223.93522222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.4 85.2544444444446 14.1455555555554 2 97.5 87.1944444444444 10.3055555555556 3 94.6 89.2144444444444 5.38555555555555 4 92.6 87.9144444444444 4.68555555555555 5 92.5 86.5344444444444 5.96555555555558 6 89.8 85.8144444444444 3.98555555555556 7 88.8 85.9344444444444 2.86555555555556 8 87.4 85.5344444444444 1.86555555555557 9 85.2 86.1344444444444 -0.934444444444437 10 83.1 84.0316666666667 -0.931666666666675 11 84.7 86.2316666666667 -1.53166666666666 12 84.8 88.0916666666667 -3.29166666666667 13 85.8 94.0044444444444 -8.20444444444439 14 86.3 95.9444444444445 -9.64444444444446 15 89 97.9644444444444 -8.96444444444444 16 89 96.6644444444444 -7.66444444444444 17 89.3 95.2844444444444 -5.98444444444445 18 91.9 94.5644444444444 -2.66444444444444 19 94.9 94.6844444444445 0.215555555555560 20 94.4 94.2844444444444 0.115555555555559 21 96.8 94.8844444444444 1.91555555555555 22 96.9 92.7816666666667 4.11833333333334 23 98 94.9816666666667 3.01833333333333 24 97.9 96.8416666666667 1.05833333333333 25 100.9 102.754444444444 -1.85444444444439 26 103.9 104.694444444444 -0.794444444444466 27 103.1 106.714444444444 -3.61444444444445 28 102.5 105.414444444444 -2.91444444444444 29 104.3 104.034444444444 0.265555555555549 30 102.6 103.314444444444 -0.714444444444446 31 101.7 103.434444444444 -1.73444444444444 32 102.8 103.034444444444 -0.234444444444451 33 105.4 103.634444444444 1.76555555555556 34 110.9 117.545555555556 -6.64555555555555 35 113.5 119.745555555556 -6.24555555555555 36 116.3 121.605555555556 -5.30555555555556 37 124 127.518333333333 -3.51833333333328 38 128.8 129.458333333333 -0.658333333333343 39 133.5 131.478333333333 2.02166666666667 40 132.6 130.178333333333 2.42166666666667 41 128.4 128.798333333333 -0.398333333333326 42 127.3 128.078333333333 -0.778333333333338 43 126.7 128.198333333333 -1.49833333333333 44 123.3 127.798333333333 -4.49833333333334 45 123.2 128.398333333333 -5.19833333333333 46 124.4 126.295555555556 -1.89555555555555 47 128.2 128.495555555556 -0.295555555555568 48 128.7 130.355555555556 -1.65555555555558 49 135.7 136.268333333333 -0.568333333333296 50 139 138.208333333333 0.79166666666664 51 145.4 140.228333333333 5.17166666666667 52 142.4 138.928333333333 3.47166666666667 53 137.7 137.548333333333 0.151666666666652 54 137 136.828333333333 0.171666666666659 55 137.1 136.948333333333 0.151666666666655 56 139.3 136.548333333333 2.75166666666667 57 139.6 137.148333333333 2.45166666666666 58 140.4 135.045555555556 5.35444444444444 59 142.3 137.245555555556 5.05444444444445 60 148.3 139.105555555556 9.19444444444444 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.79973829618494 0.40052340763012 0.20026170381506 18 0.907589144038642 0.184821711922716 0.092410855961358 19 0.977184554634248 0.0456308907315033 0.0228154453657516 20 0.991076032733663 0.0178479345326743 0.00892396726633714 21 0.998803425063 0.00239314987400105 0.00119657493700053 22 0.999907729334212 0.000184541331576458 9.22706657882291e-05 23 0.999985268015236 2.9463969527138e-05 1.4731984763569e-05 24 0.999990801414026 1.8397171948115e-05 9.1985859740575e-06 25 0.999977301912073 4.53961758535532e-05 2.26980879267766e-05 26 0.999954758681973 9.04826360539981e-05 4.52413180269990e-05 27 0.999979277973771 4.14440524574243e-05 2.07220262287121e-05 28 0.999991672165994 1.66556680118763e-05 8.32783400593815e-06 29 0.999978625943594 4.27481128123038e-05 2.13740564061519e-05 30 0.999942539403292 0.000114921193415341 5.74605967076705e-05 31 0.999875347148716 0.00024930570256745 0.000124652851283725 32 0.999711098667673 0.000577802664654345 0.000288901332327173 33 0.999309772659689 0.00138045468062291 0.000690227340311456 34 0.998268322959255 0.00346335408148993 0.00173167704074496 35 0.996111191067047 0.00777761786590666 0.00388880893295333 36 0.992937848184124 0.0141243036317519 0.00706215181587595 37 0.984659129834189 0.0306817403316220 0.0153408701658110 38 0.975682380031881 0.0486352399362382 0.0243176199681191 39 0.96028806741831 0.0794238651633807 0.0397119325816903 40 0.94700565539025 0.105988689219500 0.0529943446097501 41 0.936324650221557 0.127350699556886 0.0636753497784432 42 0.935725707887054 0.128548584225893 0.0642742921129464 43 0.961913408660055 0.0761731826798897 0.0380865913399448 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.555555555555556 NOK 5% type I error level 20 0.740740740740741 NOK 10% type I error level 22 0.814814814814815 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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