lin regr wlh

*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: Wed, 30 Dec 2009 14:04:38 -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/30/t126220713246yzdp2sjsrn6ao.htm/, Retrieved Wed, 30 Dec 2009 22:05:43 +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/30/t126220713246yzdp2sjsrn6ao.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:

» Textbox « » Textfile « » CSV «

612613 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1 506174 1 501866 1 516141 1 528222 1 532638 1 536322 1 536535 1 523597 1 536214 1 586570 1 596594 1

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 wlh[t] = + 593909.321428571 -68141.2589285715dummies[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) 593909.321428571 4729.236545 125.5825 0 0 dummies -68141.2589285715 6475.773839 -10.5225 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.810086930890089 R-squared 0.656240835598924 Adjusted R-squared 0.650313953454078 F-TEST (value) 110.722774565304 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 4.55191440096314e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25024.7675796097 Sum Squared Residuals 36321861559.9821 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 612613 593909.321428572 18703.6785714283 2 611324 593909.321428571 17414.6785714287 3 594167 593909.321428571 257.678571428578 4 595454 593909.321428571 1544.67857142858 5 590865 593909.321428571 -3044.32142857142 6 589379 593909.321428571 -4530.32142857142 7 584428 593909.321428571 -9481.32142857142 8 573100 593909.321428571 -20809.3214285714 9 567456 593909.321428571 -26453.3214285714 10 569028 593909.321428571 -24881.3214285714 11 620735 593909.321428571 26825.6785714286 12 628884 593909.321428571 34974.6785714286 13 628232 593909.321428571 34322.6785714286 14 612117 593909.321428571 18207.6785714286 15 595404 593909.321428571 1494.67857142858 16 597141 593909.321428571 3231.67857142858 17 593408 593909.321428571 -501.321428571422 18 590072 593909.321428571 -3837.32142857142 19 579799 593909.321428571 -14110.3214285714 20 574205 593909.321428571 -19704.3214285714 21 572775 593909.321428571 -21134.3214285714 22 572942 593909.321428571 -20967.3214285714 23 619567 593909.321428571 25657.6785714286 24 625809 593909.321428571 31899.6785714286 25 619916 593909.321428571 26006.6785714286 26 587625 593909.321428571 -6284.32142857142 27 565742 593909.321428571 -28167.3214285714 28 557274 593909.321428571 -36635.3214285714 29 560576 525768.0625 34807.9375 30 548854 525768.0625 23085.9375 31 531673 525768.0625 5904.9375 32 525919 525768.0625 150.937499999998 33 511038 525768.0625 -14730.0625 34 498662 525768.0625 -27106.0625 35 555362 525768.0625 29593.9375 36 564591 525768.0625 38822.9375 37 541657 525768.0625 15888.9375 38 527070 525768.0625 1301.93750000000 39 509846 525768.0625 -15922.0625 40 514258 525768.0625 -11510.0625 41 516922 525768.0625 -8846.0625 42 507561 525768.0625 -18207.0625 43 492622 525768.0625 -33146.0625 44 490243 525768.0625 -35525.0625 45 469357 525768.0625 -56411.0625 46 477580 525768.0625 -48188.0625 47 528379 525768.0625 2610.9375 48 533590 525768.0625 7821.9375 49 517945 525768.0625 -7823.0625 50 506174 525768.0625 -19594.0625 51 501866 525768.0625 -23902.0625 52 516141 525768.0625 -9627.0625 53 528222 525768.0625 2453.9375 54 532638 525768.0625 6869.9375 55 536322 525768.0625 10553.9375 56 536535 525768.0625 10766.9375 57 523597 525768.0625 -2171.0625 58 536214 525768.0625 10445.9375 59 586570 525768.0625 60801.9375 60 596594 525768.0625 70825.9375 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.110389374182019 0.220778748364038 0.889610625817981 6 0.059674253323524 0.119348506647048 0.940325746676476 7 0.0409699056805903 0.0819398113611806 0.95903009431941 8 0.0594576698988827 0.118915339797765 0.940542330101117 9 0.0861936117236736 0.172387223447347 0.913806388276326 10 0.0870760422745861 0.174152084549172 0.912923957725414 11 0.136268985939712 0.272537971879424 0.863731014060288 12 0.231828467312890 0.463656934625779 0.76817153268711 13 0.301196759433631 0.602393518867262 0.698803240566369 14 0.252525267810441 0.505050535620881 0.74747473218956 15 0.183296251598860 0.366592503197719 0.81670374840114 16 0.128330473683568 0.256660947367135 0.871669526316432 17 0.0874019903418335 0.174803980683667 0.912598009658167 18 0.0589294882361757 0.117858976472351 0.941070511763824 19 0.0466778518158410 0.0933557036316821 0.95332214818416 20 0.0427731849720544 0.0855463699441087 0.957226815027946 21 0.040031906206811 0.080063812413622 0.959968093793189 22 0.0366340533903193 0.0732681067806386 0.96336594660968 23 0.0399496317185674 0.0798992634371348 0.960050368281433 24 0.0583384810397708 0.116676962079542 0.94166151896023 25 0.0733881117965629 0.146776223593126 0.926611888203437 26 0.0565621237104365 0.113124247420873 0.943437876289564 27 0.0597288325871387 0.119457665174277 0.940271167412861 28 0.0745284888552737 0.149056977710547 0.925471511144726 29 0.0664188823688706 0.132837764737741 0.93358111763113 30 0.0532623323498306 0.106524664699661 0.94673766765017 31 0.0422020144155915 0.084404028831183 0.957797985584409 32 0.0321991103469591 0.0643982206939182 0.96780088965304 33 0.0304116772954133 0.0608233545908267 0.969588322704587 34 0.0376653771154318 0.0753307542308637 0.962334622884568 35 0.0399392740418073 0.0798785480836147 0.960060725958193 36 0.0582756785684583 0.116551357136917 0.941724321431542 37 0.0441824242012558 0.0883648484025115 0.955817575798744 38 0.0301944219872759 0.0603888439745519 0.969805578012724 39 0.0253421956457873 0.0506843912915745 0.974657804354213 40 0.0183438642656281 0.0366877285312561 0.981656135734372 41 0.0121661596753320 0.0243323193506639 0.987833840324668 42 0.00949640051572839 0.0189928010314568 0.990503599484272 43 0.0127912201518602 0.0255824403037204 0.98720877984814 44 0.0185914371072900 0.0371828742145799 0.98140856289271 45 0.0882793615036148 0.176558723007230 0.911720638496385 46 0.229029036053467 0.458058072106933 0.770970963946533 47 0.169125165586432 0.338250331172864 0.830874834413568 48 0.119250233186993 0.238500466373986 0.880749766813007 49 0.0889955079258087 0.177991015851617 0.911004492074191 50 0.0918979935426621 0.183795987085324 0.908102006457338 51 0.130359471979963 0.260718943959925 0.869640528020037 52 0.128067399059807 0.256134798119614 0.871932600940193 53 0.097398326310036 0.194796652620072 0.902601673689964 54 0.0674388721475106 0.134877744295021 0.93256112785249 55 0.0418593098695297 0.0837186197390595 0.95814069013047 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 5 0.0980392156862745 NOK 10% type I error level 20 0.392156862745098 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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