b-r0245787

*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: Tue, 21 Dec 2010 11:49:46 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932087ptgf9063e8j3gcj.htm/, Retrieved Tue, 21 Dec 2010 12:48:28 +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/2010/Dec/21/t1292932087ptgf9063e8j3gcj.htm/}, year = {2010}, } @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 = {2010}, 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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0.86 2.0 0.88 2.3 0.93 2.8 0.98 2.4 0.97 2.3 1.03 2.7 1.06 2.7 1.06 2.9 1.08 3.0 1.09 2.2 1.04 2.3 1.00 2.8 1.01 2.8 1.02 2.8 1.04 2.2 1.06 2.6 1.06 2.8 1.06 2.5 1.06 2.4 1.06 2.3 1.02 1.9 0.98 1.7 0.99 2.0 0.99 2.1 0.94 1.7 0.96 1.8 0.98 1.8 1.01 1.8 1.01 1.3 1.02 1.3 1.04 1.3 1.03 1.2 1.05 1.4 1.08 2.2 1.17 2.9 1.11 3.1 1.11 3.5 1.11 3.6 1.11 4.4 1.21 4.1 1.31 5.1 1.37 5.8 1.37 5.9 1.26 5.4 1.23 5.5 1.17 4.8 1.06 3.2 0.95 2.7 0.92 2.1 0.92 1.9 0.90 0.6 0.93 0.7 0.93 -0.2 0.97 -1.0 0.96 -1.7 0.99 -0.7 0.98 -1.0 0.96 -0.9 1.00 0.0 0.99 0.3 1.03 0.8

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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Dieselprijs[t] = + 0.850881296135343 + 0.0551712842435391Inflatie[t] + 0.00217191079112509t + 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) 0.850881296135343 0.022206 38.3177 0 0 Inflatie 0.0551712842435391 0.005085 10.8504 0 0 t 0.00217191079112509 0.00047 4.6234 2.2e-05 1.1e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.82170726122344 R-squared 0.675202823147327 Adjusted R-squared 0.664002920497235 F-TEST (value) 60.2864903599649 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 6.88338275267597e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0620745026925834 Sum Squared Residuals 0.223488145302830 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.86 0.963395775413547 -0.103395775413547 2 0.88 0.982119071477734 -0.102119071477734 3 0.93 1.01187662439063 -0.0818766243906285 4 0.98 0.991980021484338 -0.0119800214843379 5 0.97 0.98863480385111 -0.0186348038511091 6 1.03 1.01287522833965 0.0171247716603502 7 1.06 1.01504713913077 0.0449528608692251 8 1.06 1.02825330677061 0.0317466932293922 9 1.08 1.03594234598609 0.0440576540139132 10 1.09 0.99397722938238 0.0960227706176194 11 1.04 1.00166626859786 0.0383337314021404 12 1 1.03142382151075 -0.0314238215107543 13 1.01 1.03359573230188 -0.0235957323018794 14 1.02 1.03576764309300 -0.0157676430930045 15 1.04 1.00483678333801 0.0351632166619939 16 1.06 1.02907720782655 0.0309227921734532 17 1.06 1.04228337546638 0.0177166245336203 18 1.06 1.02790390098444 0.0320960990155569 19 1.06 1.02455868335121 0.0354413166487858 20 1.06 1.02121346571799 0.0387865342820146 21 1.02 1.00131686281169 0.0186831371883051 22 0.98 0.992454516754112 -0.0124545167541122 23 0.99 1.0111778128183 -0.021177812818299 24 0.99 1.01886685203378 -0.0288668520337780 25 0.94 0.998970249127487 -0.0589702491274875 26 0.96 1.00665928834297 -0.0466592883429665 27 0.98 1.00883119913409 -0.0288311991340916 28 1.01 1.01100310992522 -0.00100310992521664 29 1.01 0.985589378594572 0.0244106214054278 30 1.02 0.987761289385697 0.0322387106143028 31 1.04 0.989933200176822 0.0500667998231777 32 1.03 0.986587982543593 0.0434120174564065 33 1.05 0.999794150183426 0.0502058498165736 34 1.08 1.04610308836938 0.0338969116306172 35 1.17 1.08689489813099 0.0831051018690146 36 1.11 1.10010106577082 0.00989893422918181 37 1.11 1.12434149025936 -0.0143414902593589 38 1.11 1.13203052947484 -0.0220305294748379 39 1.11 1.17833946766079 -0.0683394676607944 40 1.21 1.16395999317886 0.0460400068211422 41 1.31 1.22130318821352 0.088696811786478 42 1.37 1.26209499797512 0.107905002024876 43 1.37 1.26978403719060 0.100215962809397 44 1.26 1.24437030585996 0.0156296941400409 45 1.23 1.25205934507544 -0.0220593450754381 46 1.17 1.21561135689609 -0.0456113568960858 47 1.06 1.12950921289755 -0.0695092128975482 48 0.95 1.10409548156690 -0.154095481566904 49 0.92 1.07316462181191 -0.153164621811905 50 0.92 1.06430227575432 -0.144302275754323 51 0.9 0.994751517028847 -0.0947515170288468 52 0.93 1.00244055624433 -0.0724405562443258 53 0.93 0.954958311216266 -0.0249583112162656 54 0.97 0.91299319461256 0.0570068053874405 55 0.96 0.876545206433207 0.0834547935667928 56 0.99 0.933888401467871 0.0561115985321286 57 0.98 0.919508926985935 0.0604910730140652 58 0.96 0.927197966201414 0.0328020337985862 59 1 0.979024032811724 0.0209759671882759 60 0.99 0.99774732887591 -0.00774732887591092 61 1.03 1.02750488178881 0.00249511821119445 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.036685673929499 0.073371347858998 0.96331432607050 7 0.0089803639576595 0.017960727915319 0.99101963604234 8 0.00682979986328786 0.0136595997265757 0.993170200136712 9 0.00407747199028292 0.00815494398056584 0.995922528009717 10 0.00168762134593226 0.00337524269186452 0.998312378654068 11 0.0137429942485713 0.0274859884971426 0.986257005751429 12 0.194242714214086 0.388485428428172 0.805757285785914 13 0.290380443632779 0.580760887265559 0.709619556367221 14 0.300707473918226 0.601414947836451 0.699292526081774 15 0.225333739769019 0.450667479538038 0.774666260230981 16 0.165579236611660 0.331158473223319 0.83442076338834 17 0.125998736156378 0.251997472312757 0.874001263843622 18 0.0882251535272634 0.176450307054527 0.911774846472737 19 0.0599792935415949 0.119958587083190 0.940020706458405 20 0.039750332629221 0.079500665258442 0.96024966737078 21 0.0273015140949608 0.0546030281899215 0.97269848590504 22 0.0219603749357815 0.0439207498715629 0.978039625064218 23 0.01969215504709 0.03938431009418 0.98030784495291 24 0.0189725699372778 0.0379451398745555 0.981027430062722 25 0.0218616206287007 0.0437232412574015 0.9781383793713 26 0.0201352962749439 0.0402705925498878 0.979864703725056 27 0.0148800774846819 0.0297601549693638 0.985119922515318 28 0.00930921733746641 0.0186184346749328 0.990690782662534 29 0.0074044565915738 0.0148089131831476 0.992595543408426 30 0.00542702452938614 0.0108540490587723 0.994572975470614 31 0.00425758630161056 0.00851517260322112 0.99574241369839 32 0.00283273148059571 0.00566546296119142 0.997167268519404 33 0.00177560259218233 0.00355120518436466 0.998224397407818 34 0.000980797226130488 0.00196159445226098 0.99901920277387 35 0.000779152458295543 0.00155830491659109 0.999220847541704 36 0.000707336928375303 0.00141467385675061 0.999292663071625 37 0.000682656016385487 0.00136531203277097 0.999317343983614 38 0.000517886807018688 0.00103577361403738 0.999482113192981 39 0.000671998985148146 0.00134399797029629 0.999328001014852 40 0.00049982774717798 0.00099965549435596 0.999500172252822 41 0.00103003653461516 0.00206007306923032 0.998969963465385 42 0.00408380927322861 0.00816761854645722 0.995916190726771 43 0.0288220897502912 0.0576441795005824 0.97117791024971 44 0.0734229208010709 0.146845841602142 0.926577079198929 45 0.227950018482882 0.455900036965764 0.772049981517118 46 0.782290298795539 0.435419402408922 0.217709701204461 47 0.998851493830339 0.00229701233932198 0.00114850616966099 48 0.99981901961442 0.000361960771161292 0.000180980385580646 49 0.99974158914474 0.000516821710519049 0.000258410855259525 50 0.99947085778815 0.00105828442369916 0.000529142211849578 51 0.998861081457499 0.00227783708500169 0.00113891854250084 52 0.996174299229436 0.00765140154112818 0.00382570077056409 53 0.998963340483594 0.00207331903281151 0.00103665951640576 54 0.99795604464667 0.00408791070666003 0.00204395535333001 55 0.989728874100148 0.0205422517997043 0.0102711258998522 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.44 NOK 5% type I error level 35 0.7 NOK 10% type I error level 39 0.78 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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