*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 08:03:40 -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/t12587294988w2s60ky0l765yr.htm/, Retrieved Fri, 20 Nov 2009 16:05:10 +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/t12587294988w2s60ky0l765yr.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:

WS7,MR4

Dataseries X:

» Textbox « » Textfile « » CSV «

1,1 2,1 1,2 1,3 1,4 2,5 1,1 1,2 1,2 2,2 1,4 1,1 1,5 2,3 1,2 1,4 1,1 2,3 1,5 1,2 1,3 2,2 1,1 1,5 1,5 2,2 1,3 1,1 1,1 1,6 1,5 1,3 1,4 1,8 1,1 1,5 1,3 1,7 1,4 1,1 1,5 1,9 1,3 1,4 1,6 1,8 1,5 1,3 1,7 1,9 1,6 1,5 1,1 1,5 1,7 1,6 1,6 1 1,1 1,7 1,3 0,8 1,6 1,1 1,7 1,1 1,3 1,6 1,6 1,5 1,7 1,3 1,7 1,7 1,6 1,7 1,9 2,3 1,7 1,6 1,8 2,4 1,9 1,7 1,9 3 1,8 1,9 1,6 3 1,9 1,8 1,5 3,2 1,6 1,9 1,6 3,2 1,5 1,6 1,6 3,2 1,6 1,5 1,7 3,5 1,6 1,6 2 4 1,7 1,6 2 4,3 2 1,7 1,9 4,1 2 2 1,7 4 1,9 2 1,8 4,1 1,7 1,9 1,9 4,2 1,8 1,7 1,7 4,5 1,9 1,8 2 5,6 1,7 1,9 2,1 6,5 2 1,7 2,4 7,6 2,1 2 2,5 8,5 2,4 2,1 2,5 8,7 2,5 2,4 2,6 8,3 2,5 2,5 2,2 8,3 2,6 2,5 2,5 8,5 2,2 2,6 2,8 8,7 2,5 2,2 2,8 8,7 2,8 2,5 2,9 8,5 2,8 2,8 3 7,9 2,9 2,8 3,1 7 3 2,9 2,9 5,8 3,1 3 2,7 4,5 2,9 3,1 2,2 3,7 2,7 2,9 2,5 3,1 2,2 2,7 2,3 2,7 2,5 2,2 2,6 2,3 2,3 2,5 2,3 1,8 2,6 2,3 2,2 1,5 2,3 2,6 1,8 1,2 2,2 2,3 1,8 1 1,8 2,2

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation inflatie[t] = + 0.427930689866057 + 0.0655500588117455inflatie_levensmiddelen[t] + 0.274321206698614`Y(t+1)`[t] + 0.300108421896122`Y(t+2)`[t] + 0.00523791030173268t + 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) 0.427930689866057 0.134995 3.17 0.002555 0.001278 inflatie_levensmiddelen 0.0655500588117455 0.014409 4.5492 3.3e-05 1.6e-05 `Y(t+1)` 0.274321206698614 0.126509 2.1684 0.034727 0.017363 `Y(t+2)` 0.300108421896122 0.124582 2.4089 0.019577 0.009789 t 0.00523791030173268 0.003553 1.4744 0.146397 0.073198 Multiple Linear Regression - Regression Statistics Multiple R 0.937641068115809 R-squared 0.879170772617355 Adjusted R-squared 0.869876216664844 F-TEST (value) 94.5898628303838 F-TEST (DF numerator) 4 F-TEST (DF denominator) 52 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.194492190339018 Sum Squared Residuals 1.96701502934919 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.1 1.29015012017575 -0.190150120175748 2 1.4 1.26416509114271 0.135834908857292 3 1.2 1.30202350362089 -0.102023503620888 4 1.5 1.34898470503291 0.151015294967091 5 1.1 1.376497292965 -0.276497292965001 6 1.3 1.35548424127495 -0.0554842412749506 7 1.5 1.29554302415796 0.204456975842043 8 1.1 1.37633682489159 -0.27633682489159 9 1.4 1.34497794865545 0.0550220513445495 10 1.3 1.30591384632714 -0.00591384632714398 11 1.5 1.3868621742902 0.113137825709799 12 1.6 1.41039847786087 0.189601522139130 13 1.7 1.50964519909286 0.190354800907137 14 1.1 1.54610604872937 -0.446106048729371 15 1.6 1.38398704779567 0.216012952204326 16 1.3 1.33321049654669 -0.0332104965466920 17 1.7 1.42587127343043 0.274128726569575 18 1.6 1.47702516336746 0.122974836632535 19 1.7 1.58798433352013 0.112015666479866 20 1.9 1.62997355758916 0.270026442410837 21 1.8 1.72664155730141 0.0733584426985947 22 1.9 1.80379906659955 0.0962009334004516 23 1.6 1.80645825538153 -0.20645825538153 24 1.5 1.77252065762564 -0.27252065762564 25 1.6 1.66029392068867 -0.0602939206886746 26 1.6 1.66295310947066 -0.0629531094706565 27 1.7 1.71786687960552 -0.0178668796055251 28 2 1.78331193998299 0.216688060017008 29 2 1.92052207212744 0.0794779278725556 30 1.9 2.00268249723566 -0.102682497235665 31 1.7 1.97393328098636 -0.273933280986361 32 1.8 1.90085111363993 -0.100851113639934 33 1.9 1.88005446611348 0.0199455338865220 34 1.7 1.96240035691821 -0.262400356918208 35 2 2.01488993276275 -0.0148899327627497 36 2.1 2.10139757362541 -0.00139757362541303 37 2.4 2.29620519585876 0.103794804141236 38 2.5 2.47274536329026 0.0272546367097364 39 2.5 2.60855793259304 -0.108557932593043 40 2.6 2.61758666155969 -0.0175866615596900 41 2.2 2.65025669253128 -0.450256692531284 42 2.5 2.58888697410553 -0.0888869741055326 43 2.8 2.56948788942075 0.23051211057925 44 2.8 2.7470546883009 0.0529453116990967 45 2.9 2.82921511340912 0.0707848865908768 46 3 2.82255510909367 0.17744489090633 47 3.1 2.82624092932431 0.273759070675694 48 2.9 2.81026173191142 0.0897382680885825 49 2.7 2.70543116660777 -0.00543116660777018 50 2.2 2.54334310414116 -0.343343104141159 51 2.5 2.31206869142731 0.187931308572686 52 2.3 2.22332872926587 0.0766712707341285 53 2.6 2.23751490127202 0.362485098727981 54 2.3 2.23225245979824 0.0677475402017604 55 2.2 2.2255615170157 -0.0255615170157007 56 1.8 2.09366976243521 -0.293669762435212 57 1.8 1.94605833610554 -0.146058336105538 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.355927954093703 0.711855908187406 0.644072045906297 9 0.204473922060758 0.408947844121516 0.795526077939242 10 0.112596983033433 0.225193966066866 0.887403016966567 11 0.0641841871537202 0.128368374307440 0.93581581284628 12 0.0959560060139252 0.191912012027850 0.904043993986075 13 0.0885050630567951 0.177010126113590 0.911494936943205 14 0.187348652792774 0.374697305585547 0.812651347207226 15 0.200148802098520 0.400297604197039 0.79985119790148 16 0.139927578679711 0.279855157359423 0.860072421320289 17 0.134238507787149 0.268477015574298 0.865761492212851 18 0.0894532848445683 0.178906569689137 0.910546715155432 19 0.063877415336593 0.127754830673186 0.936122584663407 20 0.060461883956804 0.120923767913608 0.939538116043196 21 0.0422163666131195 0.084432733226239 0.95778363338688 22 0.0561132422384892 0.112226484476978 0.943886757761511 23 0.176610381519666 0.353220763039331 0.823389618480334 24 0.532429119984875 0.93514176003025 0.467570880015125 25 0.546631854330717 0.906736291338565 0.453368145669283 26 0.487864338893522 0.975728677787044 0.512135661106478 27 0.410219441982036 0.820438883964071 0.589780558017964 28 0.477608196492944 0.955216392985887 0.522391803507056 29 0.453142589718071 0.906285179436143 0.546857410281929 30 0.376165573300614 0.752331146601228 0.623834426699386 31 0.367963817863539 0.735927635727077 0.632036182136462 32 0.308691010972414 0.617382021944827 0.691308989027586 33 0.261314777760257 0.522629555520514 0.738685222239743 34 0.251805464993036 0.503610929986073 0.748194535006964 35 0.198514350601604 0.397028701203208 0.801485649398396 36 0.155758452302972 0.311516904605944 0.844241547697028 37 0.187593355314112 0.375186710628224 0.812406644685888 38 0.173142656991653 0.346285313983306 0.826857343008347 39 0.123250509051538 0.246501018103076 0.876749490948462 40 0.101137343220204 0.202274686440407 0.898862656779796 41 0.24725932576506 0.49451865153012 0.75274067423494 42 0.230948681124250 0.461897362248501 0.76905131887575 43 0.207895693528797 0.415791387057594 0.792104306471203 44 0.206288477790166 0.412576955580331 0.793711522209834 45 0.201351177431373 0.402702354862745 0.798648822568627 46 0.174438286937576 0.348876573875153 0.825561713062424 47 0.133019526255886 0.266039052511773 0.866980473744114 48 0.114638242323433 0.229276484646867 0.885361757676567 49 0.42352275370867 0.84704550741734 0.57647724629133 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 0 0 OK 10% type I error level 1 0.0238095238095238 OK

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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