*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: Tue, 24 Nov 2009 04:34:57 -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/24/t1259063254rbqmlg6qdwrghxm.htm/, Retrieved Tue, 24 Nov 2009 12:47:50 +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/24/t1259063254rbqmlg6qdwrghxm.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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97.4 116.7 97 109 105.4 119.5 102.7 115.1 98.1 107.1 104.5 109.7 87.4 110.4 89.9 105 109.8 115.8 111.7 116.4 98.6 111.1 96.9 119.5 95.1 110.9 97 115.1 112.7 125.2 102.9 116 97.4 112.9 111.4 121.7 87.4 123.2 96.8 116.6 114.1 136.2 110.3 120.9 103.9 119.6 101.6 125.9 94.6 116.1 95.9 107.5 104.7 116.7 102.8 112.5 98.1 113 113.9 126.4 80.9 114.1 95.7 112.5 113.2 112.4 105.9 113.1 108.8 116.3 102.3 111.7 99 118.8 100.7 116.5 115.5 125.1 100.7 113.1 109.9 119.6 114.6 114.4 85.4 114 100.5 117.8 114.8 117 116.5 120.9 112.9 115 102 117.3 106 119.4 105.3 114.9 118.8 125.8 106.1 117.6 109.3 117.6 117.2 114.9 92.5 121.9 104.2 117 112.5 106.4 122.4 110.5 113.3 113.6 100 114.2

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation ipchn[t] = + 72.0310065429256 + 0.454345599215138Tip[t] -0.367700417679697M1[t] -4.49300307308312M2[t] -0.194193207476405M3[t] -3.98677708605355M4[t] -4.58869119843028M5[t] -5.64310424677002M6[t] + 5.2881430931375M7[t] -2.51335481846447M8[t] -5.75753778233051M9[t] -7.17562366995377M10[t] -5.75315845855307M11[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) 72.0310065429256 15.543362 4.6342 2.9e-05 1.4e-05 Tip 0.454345599215138 0.1529 2.9715 0.004659 0.00233 M1 -0.367700417679697 3.236915 -0.1136 0.910042 0.455021 M2 -4.49300307308312 3.22724 -1.3922 0.170411 0.085205 M3 -0.194193207476405 3.623232 -0.0536 0.957484 0.478742 M4 -3.98677708605355 3.242583 -1.2295 0.225002 0.112501 M5 -4.58869119843028 3.234822 -1.4185 0.162633 0.081317 M6 -5.64310424677002 3.688326 -1.53 0.132722 0.066361 M7 5.2881430931375 3.853389 1.3723 0.176473 0.088237 M8 -2.51335481846447 3.255927 -0.7719 0.444019 0.222009 M9 -5.75753778233051 3.730818 -1.5432 0.12948 0.06474 M10 -7.17562366995377 3.768407 -1.9042 0.063022 0.031511 M11 -5.75315845855307 3.390656 -1.6968 0.096355 0.048177 Multiple Linear Regression - Regression Statistics Multiple R 0.570122019367822 R-squared 0.325039116968044 Adjusted R-squared 0.152708678747119 F-TEST (value) 1.88613874788242 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.0610475160037202 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.09179673527599 Sum Squared Residuals 1218.54051768826 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 116.7 115.916567488801 0.783432511199086 2 109 111.609526593711 -2.60952659371103 3 119.5 119.724839492725 -0.224839492724873 4 115.1 114.705522496267 0.394477503733143 5 107.1 112.013618627500 -4.91361862750048 6 109.7 113.867017414138 -4.16701741413762 7 110.4 117.028955007466 -6.62895500746629 8 105 110.363321093902 -5.36332109390216 9 115.8 116.160615554417 -0.36061555441738 10 116.4 115.605786305303 0.794213694697134 11 111.1 111.076324166985 0.0236758330147292 12 119.5 116.057095106873 3.4429048931274 13 110.9 114.871572610606 -3.97157261060565 14 115.1 111.609526593711 3.49047340628900 15 125.2 123.041562366995 2.15843763300463 16 116 114.796391616110 1.20360838389012 17 112.9 111.69557670805 1.20442329195012 18 121.7 117.002002048722 4.69799795127792 19 123.2 117.028955007466 6.17104499253371 20 116.6 113.498305728487 3.10169427151338 21 136.2 118.114301631042 18.0856983689575 22 120.9 114.969702466402 5.93029753359833 23 119.6 113.484355842826 6.11564415717449 24 125.9 118.192519423184 7.70748057681626 25 116.1 114.644399810998 1.45560018900191 26 107.5 111.109746434574 -3.60974643457434 27 116.7 119.406797573274 -2.70679757327427 28 112.5 114.750957056188 -2.25095705618836 29 113 112.013618627500 0.98638137249952 30 126.4 118.13786604676 8.26213395324008 31 114.1 114.075708612568 0.0242913874320967 32 112.5 112.99852556935 -0.498525569349962 33 112.4 117.705390591749 -5.30539059174884 34 113.1 112.970581829855 0.129418170144920 35 116.3 115.710649278980 0.589350721020324 36 111.7 118.510561342634 -6.81056134263434 37 118.8 116.643520447545 2.15647955245531 38 116.5 113.290605310807 3.20939468919300 39 125.1 124.313730044798 0.786269955202232 40 113.1 113.796831297837 -0.696831297836579 41 119.6 117.374896698239 2.22510330176088 42 114.4 118.455907966211 -4.05590796621051 43 114 116.120263809036 -2.12026380903602 44 117.8 115.179384445583 2.62061555441737 45 117 118.432343550493 -1.43234355049306 46 120.9 117.786645181536 3.11335481846447 47 115 117.573466235762 -2.57346623576174 48 117.3 118.374257662870 -1.07425766286981 49 119.4 119.823939642051 -0.423939642050653 50 114.9 115.380595067197 -0.480595067196628 51 125.8 125.813070522208 -0.0130705222077194 52 117.6 116.250297533598 1.34970246640168 53 117.6 117.10228933871 0.497710661289967 54 114.9 119.63720652417 -4.73720652416987 55 121.9 119.346117563463 2.55388243653651 56 117 116.860463162679 0.139536837321364 57 106.4 117.387348672298 -10.9873486722982 58 110.5 120.467284216905 -9.96728421690485 59 113.6 117.755204475448 -4.1552044754478 60 114.2 117.465566464440 -3.26556646443952 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.154487878117345 0.30897575623469 0.845512121882655 17 0.160337950340942 0.320675900681883 0.839662049659058 18 0.113557224699952 0.227114449399904 0.886442775300048 19 0.333643436025001 0.667286872050001 0.666356563975 20 0.231305407696933 0.462610815393866 0.768694592303067 21 0.789551866067193 0.420896267865614 0.210448133932807 22 0.806094775227241 0.387810449545517 0.193905224772759 23 0.779402046322515 0.44119590735497 0.220597953677485 24 0.846334847492596 0.307330305014808 0.153665152507404 25 0.812065011054054 0.375869977891892 0.187934988945946 26 0.786773435992038 0.426453128015925 0.213226564007963 27 0.74462810422464 0.51074379155072 0.25537189577536 28 0.686113462240925 0.62777307551815 0.313886537759075 29 0.619425821649849 0.761148356700302 0.380574178350151 30 0.82292234727426 0.354155305451481 0.177077652725740 31 0.822881550773445 0.354236898453110 0.177118449226555 32 0.783681729348216 0.432636541303569 0.216318270651784 33 0.899709448043013 0.200581103913975 0.100290551956987 34 0.847619287019 0.304761425961998 0.152380712980999 35 0.835333469949716 0.329333060100568 0.164666530050284 36 0.891474772153852 0.217050455692297 0.108525227846148 37 0.830837899475273 0.338324201049453 0.169162100524727 38 0.763588357014529 0.472823285970942 0.236411642985471 39 0.669438800883402 0.661122398233196 0.330561199116598 40 0.569631714327734 0.860736571344531 0.430368285672266 41 0.452414236040179 0.904828472080358 0.547585763959821 42 0.367229240907505 0.73445848181501 0.632770759092495 43 0.392269638617372 0.784539277234744 0.607730361382628 44 0.248796086146082 0.497592172292163 0.751203913853918 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 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly 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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