*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, 20 Nov 2009 08:57:46 -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/Nov/20/t1258732802kye6ub8d69zjxov.htm/, Retrieved Fri, 20 Nov 2009 17:00:14 +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/Nov/20/t1258732802kye6ub8d69zjxov.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:

Dataseries X:

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100 100 97,82226485 99,87129987 94,04971502 99,54459954 91,12460521 99,81189981 93,13202153 100,4851005 93,88342812 101,1385011 92,55349954 101,3662014 94,43494835 101,5147015 96,25017563 101,8216018 100,4355715 102,4354024 101,5036685 102,5344025 99,39789728 102,6532027 99,68990733 102,4651025 101,6895041 102,4354024 103,6652759 102,4156024 103,0532766 102,4453024 100,9500712 102,8908029 102,345366 102,8512029 101,6472299 103,3561034 99,56809393 103,7422037 95,67727392 103,7224037 96,58494865 104,0788041 96,32604937 104,2075042 95,37109101 103,9105039 96,00056203 103,7026037 96,88367859 103,960004 94,85280372 104,0986041 92,46943974 104,1481041 93,99180173 104,7124047 93,45262168 104,7223047 92,26698759 105,1975052 90,39653498 105,0688051 90,43001228 105,0589051 91,04995327 105,5044055 89,07845784 105,3757054 89,69314509 105,4747055 87,92459054 106,029106 85,8789319 107,019107 83,20612366 107,3161073 83,85722053 107,7517078 83,01393462 108,5239085 82,84508195 109,3159 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation wisselkoers[t] = + 233.307819420314 -1.33554955628248consumptieprijzen[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) 233.307819420314 18.395584 12.6828 0 0 consumptieprijzen -1.33554955628248 0.173914 -7.6794 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.710040543404176 R-squared 0.504157573277698 Adjusted R-squared 0.495608565920417 F-TEST (value) 58.9726446835156 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 2.11436645969343e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.93021886529721 Sum Squared Residuals 1409.80936746449 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100 99.752863792066 0.247136207934112 2 97.82226485 99.9247491935809 -2.10248434358088 3 94.04971502 100.361073674350 -6.31135865434974 4 91.12460521 100.004080917357 -8.87947570735703 5 93.13202153 99.1049880345385 -5.97296650453847 6 93.88342812 98.2323391531338 -4.34891103313376 7 92.55349954 97.9282341185034 -5.37473457850338 8 94.43494835 97.7299048758405 -3.29495652584047 9 96.25017563 97.3200243163525 -1.06984868635251 10 100.4355715 96.5002631973766 3.93530830262341 11 101.5036685 96.3680436577497 5.13562484225034 12 99.39789728 96.2093801033534 3.18851717664659 13 99.68990733 96.460597242 3.22931008799996 14 101.6895041 96.5002631973766 5.18924090262341 15 103.6652759 96.526707078591 7.13856882140901 16 103.0532766 96.4870412567694 6.56623534323062 17 100.9500712 95.8920532616708 5.05801793832923 18 102.345366 95.9449410240995 6.40042497590045 19 101.6472299 95.2706213853578 6.37660851464225 20 99.56809393 94.7549653010122 4.8131286289878 21 95.67727392 94.7814091822266 0.8958647377734 22 96.58494865 94.3054187861477 2.27952986385229 23 96.32604937 94.1335334246992 2.19251594530081 24 95.37109101 94.53019204358 0.840898966420034 25 96.00056203 94.807853063441 1.19270896655899 26 96.88367859 94.464082206989 2.41959638301098 27 94.85280372 94.2789749049333 0.573828815066687 28 92.46943974 94.2128652018973 -1.74342546189734 29 93.99180173 93.4592137859574 0.532587944042605 30 93.45262168 93.4459918453502 0.00662983464979145 31 92.26698759 92.81133802843 -0.544350438429988 32 90.39653498 92.9832233898785 -2.58668840987849 33 90.43001228 92.9964453304857 -2.56643305048568 34 91.04995327 92.401457468942 -1.35150419894201 35 89.07845784 92.5733428303905 -3.49488499039053 36 89.69314509 92.4411232907636 -2.74797820076361 37 87.92459054 91.7006939489858 -3.77610340898583 38 85.8789319 90.3784985527166 -4.4995666527166 39 83.20612366 89.9818399338358 -6.77571627383584 40 83.85722053 89.4000738793444 -5.5428533493444 41 83.01393462 88.3687615770984 -5.35482695709839 42 82.84508195 87.311005260083 -4.46592331008302 43 78.68864276 86.9804563442382 -8.29181358423824 44 77.56959675 85.6714830221312 -8.10188627213118 45 78.53689529 84.8517217696003 -6.3148264796003 46 78.55717715 84.071626606001 -5.51444945600092 47 77.4761291 84.9839413092272 -7.50781220922723 48 81.58931659 84.7459462447427 -3.15662965474274 49 85.02428326 85.0103853239966 0.0138979360034356 50 91.71290159 85.8962561460085 5.81664544399153 51 95.96293061 86.213583121246 9.74934748875395 52 90.84689022 86.068141641012 4.77874857898807 53 92.28788036 85.5657073637186 6.72217299628136 54 95.56511274 86.411912363909 9.15320037609104 55 93.62452884 86.1078074628335 7.51672137716646 56 92.63071726 86.213583121246 6.41713413875394 57 89.50914211 86.491244141107 3.01789796889291 58 87.17171779 86.5837977253575 0.58792006464252 59 86.72624975 86.134251344048 0.591998405952063 60 85.63212844 86.5176880223215 -0.885559582321485 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.479929079355645 0.95985815871129 0.520070920644355 6 0.323949466783065 0.64789893356613 0.676050533216935 7 0.217982995632918 0.435965991265836 0.782017004367082 8 0.139198617197231 0.278397234394462 0.860801382802769 9 0.100116204657262 0.200232409314524 0.899883795342738 10 0.132228445842863 0.264456891685726 0.867771554157137 11 0.128986044308164 0.257972088616329 0.871013955691836 12 0.080784937867967 0.161569875735934 0.919215062132033 13 0.0497817805120952 0.0995635610241904 0.950218219487905 14 0.0394676172501249 0.0789352345002498 0.960532382749875 15 0.047635259829139 0.095270519658278 0.95236474017086 16 0.0431586326998295 0.086317265399659 0.95684136730017 17 0.0274748830218659 0.0549497660437318 0.972525116978134 18 0.0198712130615129 0.0397424261230258 0.980128786938487 19 0.0142841965122697 0.0285683930245394 0.98571580348773 20 0.0137988304808838 0.0275976609617675 0.986201169519116 21 0.0270633119323554 0.0541266238647108 0.972936688067645 22 0.0331645615084389 0.0663291230168779 0.966835438491561 23 0.0362006441352625 0.0724012882705251 0.963799355864738 24 0.0369682937282169 0.0739365874564339 0.963031706271783 25 0.0311473274121832 0.0622946548243665 0.968852672587817 26 0.0253446032944876 0.0506892065889752 0.974655396705512 27 0.0243455782119932 0.0486911564239863 0.975654421788007 28 0.0311115551562202 0.0622231103124404 0.96888844484378 29 0.0295600312419677 0.0591200624839353 0.970439968758032 30 0.0278015826836675 0.055603165367335 0.972198417316332 31 0.0280371672250735 0.056074334450147 0.971962832774927 32 0.0319198406606106 0.0638396813212212 0.96808015933939 33 0.0317457439091099 0.0634914878182199 0.96825425609089 34 0.0272498887073565 0.054499777414713 0.972750111292644 35 0.0265953000712182 0.0531906001424365 0.973404699928782 36 0.0225057357131662 0.0450114714263325 0.977494264286834 37 0.0200815914109683 0.0401631828219367 0.979918408589032 38 0.0183762922070337 0.0367525844140674 0.981623707792966 39 0.0232320289567030 0.0464640579134061 0.976767971043297 40 0.0254790804519042 0.0509581609038084 0.974520919548096 41 0.0370792069489186 0.0741584138978373 0.962920793051081 42 0.0529449717350824 0.105889943470165 0.947055028264917 43 0.286995328757749 0.573990657515499 0.713004671242251 44 0.489108221337385 0.97821644267477 0.510891778662615 45 0.466704052156769 0.933408104313537 0.533295947843231 46 0.376995358661403 0.753990717322806 0.623004641338597 47 0.519478923194649 0.961042153610702 0.480521076805351 48 0.551739409292992 0.896521181414016 0.448260590707008 49 0.706375813005033 0.587248373989934 0.293624186994967 50 0.674892229028196 0.650215541943609 0.325107770971804 51 0.805030889153968 0.389938221692064 0.194969110846032 52 0.724564428545442 0.550871142909116 0.275435571454558 53 0.64973651650714 0.70052696698572 0.35026348349286 54 0.832318259560017 0.335363480879967 0.167681740439983 55 0.78644901404926 0.42710197190148 0.21355098595074 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 8 0.156862745098039 NOK 10% type I error level 29 0.568627450980392 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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