Paper statistiek: Multiple Regression Analysis

*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: Fri, 11 Dec 2009 05:36:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535092ktircb0v4wpm4fa.htm/, Retrieved Fri, 11 Dec 2009 13:38:24 +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/2009/Dec/11/t1260535092ktircb0v4wpm4fa.htm/}, year = {2009}, } @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 = {2009}, 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:

ETP(33)

Dataseries X:

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1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,52 1,43 0 0 0 0 0,52 1,44 0 0 0 0 0,52 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,57 1 1 0 0 0,54 1,58 1 1 0 0 0,55 1,58 1 1 0 0 0,55 1,58 1 1 0 0 0,55 1,58 1 1 0 0 0,55 1,59 1 1 1 1 0,55 1,6 1 1 1 2 0,55 1,6 1 1 1 3 0,55 1,61 1 1 1 4 0,55 1,61 1 1 1 5 0,56 1,61 1 1 1 6 0,56 1,62 1 1 1 7 0,56 1,63 1 1 1 8 0,56 1,63 1 1 1 9 0,56 1,64 1 1 1 10 0,55 1,64 1 1 1 11 0,56 1,64 1 1 1 12 0,5 etc...

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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Broodprijzen[t] = + 1.36630284324960 + 0.048776493601080Dummy2[t] + 0.0953311220622557Dummy3[t] + 0.0162547070817098Dummy1[t] + 0.00368060742762061Dummy4[t] + 0.119420968371337Bakmeelprijzen[t] + 0.00297114816391351M1[t] + 0.002981846637013M2[t] + 0.00405876952256208M3[t] + 0.00561337628159652M4[t] + 0.00445145723040296M5[t] + 0.0040060639894374M6[t] + 0.0033347659098631M7[t] + 0.00144258471618672M8[t] + 0.00249991192643972M9[t] + 0.00331839719995005M10[t] + 0.00142035666323235M11[t] -5.18863078158954e-05t + 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) 1.36630284324960 0.043161 31.656 0 0 Dummy2 0.048776493601080 0.002086 23.3794 0 0 Dummy3 0.0953311220622557 0.002277 41.8742 0 0 Dummy1 0.0162547070817098 0.002494 6.5165 0 0 Dummy4 0.00368060742762061 0.000186 19.8365 0 0 Bakmeelprijzen 0.119420968371337 0.084259 1.4173 0.163767 0.081883 M1 0.00297114816391351 0.002211 1.344 0.186161 0.093081 M2 0.002981846637013 0.00225 1.325 0.19232 0.09616 M3 0.00405876952256208 0.002247 1.8063 0.078035 0.039018 M4 0.00561337628159652 0.002239 2.5066 0.016147 0.008073 M5 0.00445145723040296 0.002246 1.9823 0.054016 0.027008 M6 0.0040060639894374 0.002234 1.7935 0.0801 0.04005 M7 0.0033347659098631 0.002222 1.5007 0.140914 0.070457 M8 0.00144258471618672 0.002212 0.6522 0.517835 0.258917 M9 0.00249991192643972 0.002187 1.1431 0.259479 0.12974 M10 0.00331839719995005 0.002197 1.5106 0.138377 0.069188 M11 0.00142035666323235 0.002174 0.6532 0.517164 0.258582 t -5.18863078158954e-05 9e-05 -0.5796 0.565255 0.282628 Multiple Linear Regression - Regression Statistics Multiple R 0.999255190193247 R-squared 0.998510935128142 Adjusted R-squared 0.997908218394295 F-TEST (value) 1656.68361114606 F-TEST (DF numerator) 17 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.00343548434953111 Sum Squared Residuals 0.000495707214066674 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.43 1.43012679897509 -0.000126798975092287 2 1.43 1.43008561114037 -8.5611140368076e-05 3 1.43 1.43111064771810 -0.00111064771810136 4 1.43 1.43261336816932 -0.00261336816931995 5 1.43 1.43259377249402 -0.00259377249402379 6 1.43 1.43209649294524 -0.00209649294524237 7 1.44 1.43137330855785 0.00862669144214783 8 1.48 1.47939994434115 0.000600055658846702 9 1.48 1.48040538524359 -0.000405385243590406 10 1.48 1.47997777452557 2.22254744285334e-05 11 1.48 1.47802784768104 0.00197215231896213 12 1.48 1.47655560470999 0.00344439529001038 13 1.48 1.47947486656609 0.000525133433912763 14 1.48 1.47943367873137 0.000566321268629165 15 1.48 1.48045871530910 -0.000458715309104021 16 1.48 1.48196143576032 -0.00196143576032256 17 1.48 1.48074763040131 -0.000747630401313108 18 1.48 1.48025035085253 -0.00025035085253165 19 1.48 1.47952716646514 0.000472833534858542 20 1.48 1.47877730864736 0.00122269135263744 21 1.48 1.4797827495498 0.000217250450200341 22 1.48 1.48054934851549 -0.000549348515494088 23 1.48 1.47979363135467 0.000206368645326135 24 1.48 1.47832138838363 0.00167861161637438 25 1.48 1.48124065023972 -0.00124065023972324 26 1.48 1.48119946240501 -0.00119946240500683 27 1.48 1.48222449898274 -0.00222449898274002 28 1.48 1.48372721943396 -0.00372721943395856 29 1.48 1.48251341407495 -0.00251341407494911 30 1.48 1.48201613452617 -0.00201613452616765 31 1.48 1.48129295013878 -0.00129295013877746 32 1.48 1.47934888263729 0.000651117362714818 33 1.48 1.47916011385601 0.000839886143991086 34 1.48 1.47992671282170 7.32871782966574e-05 35 1.48 1.47797678597717 0.00202321402283025 36 1.48 1.47650454300612 0.00349545699387849 37 1.48 1.47942380486222 0.000576195137780881 38 1.57 1.57590794877347 -0.00590794877347171 39 1.58 1.57812719503492 0.00187280496508174 40 1.58 1.57962991548614 0.000370084513863197 41 1.58 1.57841611012713 0.00158388987287265 42 1.58 1.57791883057835 0.00208116942165411 43 1.59 1.59713096070029 -0.00713096070028606 44 1.6 1.59886750062641 0.00113249937358561 45 1.6 1.60355354895647 -0.00355354895647211 46 1.61 1.60800075534979 0.00199924465021286 47 1.61 1.61092564561659 -0.000925645616587536 48 1.61 1.61313401007316 -0.0031340100731599 49 1.62 1.61973387935688 0.000266120643121877 50 1.63 1.62337329894978 0.00662670105021745 51 1.63 1.62807894295514 0.00192105704486366 52 1.64 1.63206806115026 0.00793193884973788 53 1.64 1.63572907290259 0.00427092709741334 54 1.64 1.63771819109771 0.00228180890228756 55 1.64 1.64067561413794 -0.000675614137942863 56 1.64 1.64360636374778 -0.00360636374778458 57 1.65 1.64709820239413 0.00290179760587109 58 1.65 1.65154540878744 -0.00154540878744396 59 1.65 1.65327608937053 -0.00327608937053098 60 1.65 1.65548445382710 -0.00548445382710335 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.476659898184458 0.953319796368915 0.523340101815542 22 0.33675368942856 0.67350737885712 0.66324631057144 23 0.250091123384195 0.500182246768391 0.749908876615805 24 0.243303745029443 0.486607490058886 0.756696254970557 25 0.2526662875885 0.505332575177 0.7473337124115 26 0.182249173435121 0.364498346870243 0.817750826564879 27 0.114767636757822 0.229535273515644 0.885232363242178 28 0.0745390099790803 0.149078019958161 0.92546099002092 29 0.0420420043657852 0.0840840087315703 0.957957995634215 30 0.0269362599890882 0.0538725199781764 0.973063740010912 31 0.0417347162464472 0.0834694324928944 0.958265283753553 32 0.0234156150582309 0.0468312301164618 0.976584384941769 33 0.0120138224268929 0.0240276448537858 0.987986177573107 34 0.00596546743441551 0.0119309348688310 0.994034532565584 35 0.0024796158795913 0.0049592317591826 0.997520384120409 36 0.00272412093437857 0.00544824186875714 0.997275879065621 37 0.000999629325150405 0.00199925865030081 0.99900037067485 38 0.000901724069164878 0.00180344813832976 0.999098275930835 39 0.0088267628194109 0.0176535256388218 0.99117323718059 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.210526315789474 NOK 5% type I error level 8 0.421052631578947 NOK 10% type I error level 11 0.578947368421053 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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