Q3 - a

*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: Sun, 23 Nov 2008 11:07:18 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t12274636849r1scbb874w591e.htm/, Retrieved Sun, 23 Nov 2008 18:08:04 +0000

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/2008/Nov/23/t12274636849r1scbb874w591e.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1515 0 1510 0 1225 0 1577 0 1417 0 1224 0 1693 0 1633 0 1639 0 1914 0 1586 0 1552 0 2081 1 1500 0 1437 0 1470 0 1849 0 1387 0 1592 0 1589 0 1798 0 1935 0 1887 0 2027 1 2080 1 1556 0 1682 0 1785 0 1869 0 1781 0 2082 1 2570 1 1862 0 1936 0 1504 0 1765 0 1607 0 1577 0 1493 0 1615 0 1700 0 1335 0 1523 0 1623 0 1540 0 1637 0 1524 0 1419 0 1821 0 1593 0 1357 0 1263 0 1750 0 1405 0 1393 0 1639 0 1679 0 1551 0 1744 0 1429 0 1784 0

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Gebouwen[t] = + 1601.25 + 566.75Dummy[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) 1601.25 24.417763 65.5773 0 0 Dummy 566.75 85.287579 6.6452 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.654265223784699 R-squared 0.428062983054043 Adjusted R-squared 0.418369135309196 F-TEST (value) 44.158211921742 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 1.07556417106025e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 182.725806439548 Sum Squared Residuals 1969934.5 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1515 1601.25 -86.2499999999986 2 1510 1601.25 -91.25 3 1225 1601.25 -376.25 4 1577 1601.25 -24.2500000000000 5 1417 1601.25 -184.25 6 1224 1601.25 -377.25 7 1693 1601.25 91.75 8 1633 1601.25 31.75 9 1639 1601.25 37.75 10 1914 1601.25 312.75 11 1586 1601.25 -15.2500000000000 12 1552 1601.25 -49.25 13 2081 2168 -87 14 1500 1601.25 -101.25 15 1437 1601.25 -164.25 16 1470 1601.25 -131.25 17 1849 1601.25 247.75 18 1387 1601.25 -214.25 19 1592 1601.25 -9.25000000000002 20 1589 1601.25 -12.2500000000000 21 1798 1601.25 196.75 22 1935 1601.25 333.75 23 1887 1601.25 285.75 24 2027 2168 -141 25 2080 2168 -88 26 1556 1601.25 -45.25 27 1682 1601.25 80.75 28 1785 1601.25 183.75 29 1869 1601.25 267.75 30 1781 1601.25 179.75 31 2082 2168 -86 32 2570 2168 402 33 1862 1601.25 260.75 34 1936 1601.25 334.75 35 1504 1601.25 -97.25 36 1765 1601.25 163.75 37 1607 1601.25 5.74999999999998 38 1577 1601.25 -24.2500000000000 39 1493 1601.25 -108.25 40 1615 1601.25 13.7500000000000 41 1700 1601.25 98.75 42 1335 1601.25 -266.25 43 1523 1601.25 -78.25 44 1623 1601.25 21.75 45 1540 1601.25 -61.25 46 1637 1601.25 35.75 47 1524 1601.25 -77.25 48 1419 1601.25 -182.25 49 1821 1601.25 219.75 50 1593 1601.25 -8.25000000000002 51 1357 1601.25 -244.25 52 1263 1601.25 -338.25 53 1750 1601.25 148.75 54 1405 1601.25 -196.25 55 1393 1601.25 -208.25 56 1639 1601.25 37.75 57 1679 1601.25 77.75 58 1551 1601.25 -50.25 59 1744 1601.25 142.75 60 1429 1601.25 -172.25 61 1784 1601.25 182.75 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.484641960933697 0.969283921867394 0.515358039066303 6 0.567924218135971 0.864151563728057 0.432075781864029 7 0.679571304099826 0.640857391800347 0.320428695900174 8 0.645110997866845 0.70977800426631 0.354889002133155 9 0.598907695245897 0.802184609508205 0.401092304754103 10 0.853297242291948 0.293405515416103 0.146702757708052 11 0.789516223282086 0.420967553435828 0.210483776717914 12 0.712299871014981 0.575400257970038 0.287700128985019 13 0.628995865470159 0.742008269059682 0.371004134529841 14 0.547607056497595 0.90478588700481 0.452392943502405 15 0.495452898730127 0.990905797460255 0.504547101269872 16 0.427644137422171 0.855288274844342 0.572355862577829 17 0.564205305162918 0.871589389674164 0.435794694837082 18 0.561773099820712 0.876453800358576 0.438226900179288 19 0.484178520672922 0.968357041345843 0.515821479327078 20 0.407429925135287 0.814859850270573 0.592570074864713 21 0.452155647012805 0.90431129402561 0.547844352987195 22 0.652901805396408 0.694196389207184 0.347098194603592 23 0.748622334285569 0.502755331428862 0.251377665714431 24 0.713464001733435 0.57307199653313 0.286535998266565 25 0.68107716188451 0.63784567623098 0.31892283811549 26 0.61362922383503 0.77274155232994 0.38637077616497 27 0.554616688678678 0.890766622642645 0.445383311321322 28 0.555441608003261 0.889116783993479 0.444558391996739 29 0.637197634283744 0.725604731432513 0.362802365716256 30 0.634183559957055 0.73163288008589 0.365816440042945 31 0.702202596724337 0.595594806551327 0.297797403275663 32 0.79691222373989 0.40617555252022 0.20308777626011 33 0.850336145426672 0.299327709146655 0.149663854573328 34 0.941173390027873 0.117653219944255 0.0588266099721273 35 0.92171377549788 0.15657244900424 0.07828622450212 36 0.924453771266641 0.151092457466718 0.075546228733359 37 0.894054274090109 0.211891451819782 0.105945725909891 38 0.854213219402257 0.291573561195487 0.145786780597743 39 0.817232455152303 0.365535089695394 0.182767544847697 40 0.762700548720052 0.474598902559896 0.237299451279948 41 0.731637072440466 0.536725855119068 0.268362927559534 42 0.78457725961613 0.430845480767739 0.215422740383870 43 0.724042709107869 0.551914581784261 0.275957290892131 44 0.653615221537329 0.692769556925343 0.346384778462671 45 0.57296668893966 0.854066622120681 0.427033311060341 46 0.495504410013434 0.991008820026869 0.504495589986566 47 0.411202831644202 0.822405663288404 0.588797168355798 48 0.382042483484502 0.764084966969004 0.617957516515498 49 0.455961721956723 0.911923443913445 0.544038278043277 50 0.361342415207382 0.722684830414764 0.638657584792618 51 0.378211862184555 0.75642372436911 0.621788137815445 52 0.59498889941992 0.81002220116016 0.40501110058008 53 0.566849157488647 0.866301685022706 0.433150842511353 54 0.57141763885073 0.857164722298541 0.428582361149270 55 0.661508310301846 0.676983379396307 0.338491689698154 56 0.488712717808813 0.977425435617626 0.511287282191187 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 0 0 OK

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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