Multiple regression - goud en olieprijs

*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 16:21:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/25/t12275690406wnob3bwu0r9srn.htm/, Retrieved Mon, 24 Nov 2008 23:24:09 +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/25/t12275690406wnob3bwu0r9srn.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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10413.00 29.08 10709.00 28.76 10662.00 29.59 10570.00 30.70 10297.00 30.52 10635.00 32.67 10872.00 33.19 10296.00 37.13 10383.00 35.54 10431.00 37.75 10574.00 41.84 10653.00 42.94 10805.00 49.14 10872.00 44.61 10625.00 40.22 10407.00 44.23 10463.00 45.85 10556.00 53.38 10646.00 53.26 10702.00 51.80 11353.00 55.30 11346.00 57.81 11451.00 63.96 11964.00 63.77 12574.00 59.15 13031.00 56.12 13812.00 57.42 14544.00 63.52 14931.00 61.71 14886.00 63.01 16005.00 68.18 17064.00 72.03 15168.00 69.75 16050.00 74.41 15839.00 74.33 15137.00 64.24 14954.00 60.03 15648.00 59.44 15305.00 62.50 15579.00 55.04 16348.00 58.34 15928.00 61.92 16171.00 67.65 15937.00 67.68 15713.00 70.30 15594.00 75.26 15683.00 71.44 16438.00 76.36 17032.00 81.71 17696.00 92.60 17745.00 90.60 19394.00 92.23 20148.00 94.09 20108.00 102.79 18584.00 109.65 18441.00 124.05 18391.00 132.69 19178.00 135.81 18079.00 116.07 18483.00 101.42

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 Goudprijs[t] = + 7196.18909437676 + 107.706188015569Olieprijs[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) 7196.18909437676 541.908616 13.2793 0 0 Olieprijs 107.706188015569 7.801185 13.8064 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.875619119426176 R-squared 0.766708842304672 Adjusted R-squared 0.762686580965097 F-TEST (value) 190.616366659496 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1541.75380386152 Sum Squared Residuals 137866277.919844 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10413 10328.2850418695 84.7149581304786 2 10709 10293.8190617045 415.180938295472 3 10662 10383.2151977574 278.784802242552 4 10570 10502.7690664547 67.2309335452707 5 10297 10483.3819526119 -186.381952611927 6 10635 10714.9502568454 -79.950256845401 7 10872 10770.9574746135 101.042525386504 8 10296 11195.3198553948 -899.319855394838 9 10383 11024.0670164501 -641.067016450083 10 10431 11262.0976919645 -831.09769196449 11 10574 11702.6160009482 -1128.61600094817 12 10653 11821.0928077653 -1168.09280776529 13 10805 12488.8711734618 -1683.87117346182 14 10872 12000.9621417513 -1128.96214175129 15 10625 11528.1319763629 -903.131976362946 16 10407 11960.0337903054 -1553.03379030538 17 10463 12134.5178148906 -1671.5178148906 18 10556 12945.5454106478 -2389.54541064783 19 10646 12932.6206680860 -2286.62066808596 20 10702 12775.3696335832 -2073.36963358323 21 11353 13152.3412916377 -1799.34129163772 22 11346 13422.6838235568 -2076.68382355680 23 11451 14085.0768798526 -2634.07687985255 24 11964 14064.6127041296 -2100.61270412959 25 12574 13567.0101154977 -993.010115497665 26 13031 13240.6603658105 -209.660365810491 27 13812 13380.6784102307 431.321589769269 28 14544 14037.6861571257 506.313842874298 29 14931 13842.7379568175 1088.26204318248 30 14886 13982.7560012378 903.243998762239 31 16005 14539.5969932783 1465.40300672175 32 17064 14954.2658171382 2109.73418286181 33 15168 14708.6957084627 459.304291537304 34 16050 15210.6065446152 839.393455384753 35 15839 15201.990049574 637.009950425999 36 15137 14115.2346124969 1021.76538750309 37 14954 13661.7915609514 1292.20843904863 38 15648 13598.2449100222 2049.75508997782 39 15305 13927.8258453498 1377.17415465018 40 15579 13124.3376827537 2454.66231724632 41 16348 13479.7681032051 2868.23189679494 42 15928 13865.3562563008 2062.64374369921 43 16171 14482.51271363 1688.48728637000 44 15937 14485.7438992705 1451.25610072953 45 15713 14767.9341118713 945.065888128741 46 15594 15302.1568044285 291.843195571519 47 15683 14890.719166209 792.280833790993 48 16438 15420.6336112456 1017.36638875439 49 17032 15996.8617171289 1035.1382828711 50 17696 17169.7821046184 526.217895381555 51 17745 16954.3697285873 790.630271412692 52 19394 17129.9308150527 2264.06918494731 53 20148 17330.2643247616 2817.73567523836 54 20108 18267.3081604971 1840.69183950291 55 18584 19006.1726102839 -422.172610283897 56 18441 20557.1417177081 -2116.14171770809 57 18391 21487.7231821626 -3096.72318216260 58 19178 21823.7664887712 -2645.76648877118 59 18079 19697.6463373438 -1618.64633734385 60 18483 18119.7506829158 363.249317084236 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00189296537506119 0.00378593075012237 0.998107034624939 6 0.000299664830178450 0.0005993296603569 0.999700335169821 7 6.43554059781815e-05 0.000128710811956363 0.999935644594022 8 2.4615006321677e-05 4.9230012643354e-05 0.999975384993678 9 3.16762281663169e-06 6.33524563326338e-06 0.999996832377183 10 3.54376772050176e-07 7.08753544100352e-07 0.999999645623228 11 5.8379895781908e-08 1.16759791563816e-07 0.999999941620104 12 9.56883985497765e-09 1.91376797099553e-08 0.99999999043116 13 2.19823595555400e-09 4.39647191110801e-09 0.999999997801764 14 5.06806158529190e-10 1.01361231705838e-09 0.999999999493194 15 5.86565020372616e-11 1.17313004074523e-10 0.999999999941343 16 1.78974573615576e-11 3.57949147231152e-11 0.999999999982103 17 3.87677449409202e-12 7.75354898818404e-12 0.999999999996123 18 8.86217307850724e-13 1.77243461570145e-12 0.999999999999114 19 2.15257678727870e-13 4.30515357455740e-13 0.999999999999785 20 6.56060787076434e-14 1.31212157415287e-13 0.999999999999934 21 3.20557676340965e-12 6.4111535268193e-12 0.999999999996794 22 1.6111711733058e-11 3.2223423466116e-11 0.999999999983888 23 9.51756352790497e-11 1.90351270558099e-10 0.999999999904824 24 9.1750045392601e-09 1.83500090785202e-08 0.999999990824995 25 8.59795805085092e-06 1.71959161017018e-05 0.99999140204195 26 0.00166222292467710 0.00332444584935421 0.998337777075323 27 0.0588345240668833 0.117669048133767 0.941165475933117 28 0.280548890122869 0.561097780245738 0.719451109877131 29 0.559809256232757 0.880381487534486 0.440190743767243 30 0.704070603337372 0.591858793325255 0.295929396662628 31 0.814550797081106 0.370898405837788 0.185449202918894 32 0.903323004255051 0.193353991489898 0.0966769957449489 33 0.899606386484798 0.200787227030405 0.100393613515202 34 0.88199793120524 0.236004137589519 0.118002068794760 35 0.859849630198223 0.280300739603554 0.140150369801777 36 0.854633869238103 0.290732261523794 0.145366130761897 37 0.858452818348295 0.28309436330341 0.141547181651705 38 0.865050714439702 0.269898571120595 0.134949285560298 39 0.855005708147382 0.289988583705235 0.144994291852618 40 0.866578705160569 0.266842589678862 0.133421294839431 41 0.881263902504678 0.237472194990644 0.118736097495322 42 0.857740726892127 0.284518546215746 0.142259273107873 43 0.815696807864942 0.368606384270116 0.184303192135058 44 0.767410945503904 0.465178108992191 0.232589054496096 45 0.732972815573368 0.534054368853264 0.267027184426632 46 0.75805968392874 0.483880632142519 0.241940316071260 47 0.813490232307839 0.373019535384323 0.186509767692161 48 0.85574727392499 0.288505452150022 0.144252726075011 49 0.895946219865859 0.208107560268283 0.104053780134141 50 0.906928622213220 0.186142755573561 0.0930713777867804 51 0.955666616580168 0.0886667668396643 0.0443333834198322 52 0.913602530138123 0.172794939723754 0.086397469861877 53 0.903495860433574 0.193008279132852 0.0965041395664262 54 0.987896957605168 0.0242060847896645 0.0121030423948322 55 0.96244652473174 0.0751069505365206 0.0375534752682603 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.431372549019608 NOK 5% type I error level 23 0.450980392156863 NOK 10% type I error level 25 0.490196078431373 NOK

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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