review 7

*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 01:31:24 -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/t1259051575mne92m0vtycv5cg.htm/, Retrieved Tue, 24 Nov 2009 09:33:07 +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/t1259051575mne92m0vtycv5cg.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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6,1 0 6,2 6,3 6,3 0 6,1 6,2 6,5 0 6,3 6,1 6,6 0 6,5 6,3 6,5 0 6,6 6,5 6,2 0 6,5 6,6 6,2 0 6,2 6,5 5,9 0 6,2 6,2 6,1 0 5,9 6,2 6,1 0 6,1 5,9 6,1 0 6,1 6,1 6,1 0 6,1 6,1 6,1 0 6,1 6,1 6,4 0 6,1 6,1 6,7 0 6,4 6,1 6,9 0 6,7 6,4 7 0 6,9 6,7 7 0 7 6,9 6,8 0 7 7 6,4 0 6,8 7 5,9 0 6,4 6,8 5,5 0 5,9 6,4 5,5 0 5,5 5,9 5,6 0 5,5 5,5 5,8 0 5,6 5,5 5,9 0 5,8 5,6 6,1 0 5,9 5,8 6,1 0 6,1 5,9 6 0 6,1 6,1 6 0 6 6,1 5,9 0 6 6 5,5 0 5,9 6 5,6 0 5,5 5,9 5,4 0 5,6 5,5 5,2 0 5,4 5,6 5,2 0 5,2 5,4 5,2 0 5,2 5,2 5,5 0 5,2 5,2 5,8 1 5,5 5,2 5,8 1 5,8 5,5 5,5 1 5,8 5,8 5,3 1 5,5 5,8 5,1 1 5,3 5,5 5,2 1 5,1 5,3 5,8 1 5,2 5,1 5,8 1 5,8 5,2 5,5 1 5,8 5,8 5 1 5,5 5,8 4,9 1 5 5,5 5,3 1 4,9 5 6,1 1 5,3 4,9 6,5 1 6,1 5,3 6,8 1 6,5 6,1 6,6 1 6,8 6,5 6,4 1 6,6 6,8 6,4 1 6,4 6,6

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 15 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.989097746251875 + 0.00487608435585063x[t] + 1.40073692274530`y-1`[t] -0.574367374215303`y-2`[t] + 0.0852761437421179M1[t] + 0.289523775607878M2[t] + 0.286041328110218M3[t] + 0.0727959225051778M4[t] + 0.0651493773256329M5[t] + 0.0352599174579693M6[t] + 0.0815601084452934M7[t] -0.00106378547321905M8[t] + 0.297128142922298M9[t] -0.134853023618768M10[t] + 0.00937862150184482M11[t] -0.00168436928728821t + 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) 0.989097746251875 0.461344 2.1439 0.038169 0.019084 x 0.00487608435585063 0.092619 0.0526 0.958276 0.479138 `y-1` 1.40073692274530 0.134845 10.3877 0 0 `y-2` -0.574367374215303 0.141296 -4.065 0.000219 0.000109 M1 0.0852761437421179 0.123746 0.6891 0.494726 0.247363 M2 0.289523775607878 0.124883 2.3184 0.025626 0.012813 M3 0.286041328110218 0.134802 2.1219 0.040087 0.020043 M4 0.0727959225051778 0.141842 0.5132 0.610621 0.30531 M5 0.0651493773256329 0.136653 0.4767 0.636135 0.318067 M6 0.0352599174579693 0.135379 0.2605 0.79585 0.397925 M7 0.0815601084452934 0.133362 0.6116 0.544282 0.272141 M8 -0.00106378547321905 0.130128 -0.0082 0.993518 0.496759 M9 0.297128142922298 0.132039 2.2503 0.029998 0.014999 M10 -0.134853023618768 0.133602 -1.0094 0.318866 0.159433 M11 0.00937862150184482 0.130278 0.072 0.942969 0.471485 t -0.00168436928728821 0.002882 -0.5844 0.562264 0.281132 Multiple Linear Regression - Regression Statistics Multiple R 0.956435186436456 R-squared 0.914768265853738 Adjusted R-squared 0.88280636554889 F-TEST (value) 28.6205844185986 F-TEST (DF numerator) 15 F-TEST (DF denominator) 40 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.183690648242067 Sum Squared Residuals 1.34969017006363 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.1 6.13874398417115 -0.0387439841711496 2 6.3 6.25867029189661 0.0413297081033868 3 6.5 6.59108759708225 -0.0910875970822549 4 6.6 6.54143173189593 0.0585682681040732 5 6.5 6.55730103486056 -0.0573010348605629 6 6.2 6.32821677600955 -0.128216776009552 7 6.2 6.01004825830753 0.189951741692472 8 5.9 6.09805020736632 -0.198050207366318 9 6.1 5.97433668965096 0.125663310349041 10 6.1 5.99312875063625 0.106871249363746 11 6.1 6.02080255162652 0.0791974483734817 12 6.1 6.00973956083739 0.0902604391626146 13 6.1 6.09333133529221 0.00666866470778512 14 6.4 6.29589459787069 0.104105402129314 15 6.7 6.71094885790933 -0.0109488579093281 16 6.9 6.743929947576 0.156070052424002 17 7 6.84243620539363 0.157563794606366 18 7 6.83606259367015 0.163937406329849 19 6.8 6.82324167794866 -0.0232416779486567 20 6.4 6.4587860301938 -0.0587860301937957 21 5.9 6.30987229504697 -0.409872295046968 22 5.5 5.40558524753209 0.0944147524679146 23 5.5 5.27502144137494 0.224978558625058 24 5.6 5.49370540027193 0.10629459972807 25 5.8 5.71737086700129 0.0826291329987112 26 5.9 6.14264477670729 -0.242644776707289 27 6.1 6.16267817735381 -0.0626781773538121 28 6.1 6.17045904958901 -0.0704590495890119 29 6 6.04625466027912 -0.0462546602791184 30 6 5.87460713884964 0.125392861150363 31 5.9 5.9766596979712 -0.0766596979712029 32 5.5 5.75227774249087 -0.252277742490873 33 5.6 5.54592726992251 0.0540727300774864 34 5.4 5.48208237605481 -0.0820823760548086 35 5.2 5.28704552991755 -0.0870455299175448 36 5.2 5.11070862942241 0.0892913705775878 37 5.2 5.3091738787203 -0.109173878720302 38 5.5 5.51173714129877 -0.0117371412987739 39 5.8 5.93166748569327 -0.131667485693266 40 5.8 5.96464857535994 -0.164648575359936 41 5.5 5.78300744862851 -0.283007448628513 42 5.3 5.33121254264997 -0.0312125426499719 43 5.1 5.26799119206554 -0.167991192065539 44 5.2 5.01840901915374 0.181590980846262 45 5.8 5.56986374537956 0.230136254620441 46 5.8 5.91920362577685 -0.119203625776852 47 5.5 5.717130477081 -0.217130477080995 48 5 5.28584640946827 -0.285846409468273 49 4.9 4.84137993481504 0.0586200651849557 50 5.3 5.19105319222664 0.108946807773362 51 6.1 5.80361788196134 0.296382118038661 52 6.5 6.47953069557913 0.0204693044208727 53 6.8 6.57100065083817 0.228999349161828 54 6.6 6.72990094882069 -0.129900948820688 55 6.4 6.32205917370707 0.077940826292927 56 6.4 6.07247700079528 0.327522999204726 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.201967753741900 0.403935507483799 0.7980322462581 20 0.165174100137253 0.330348200274506 0.834825899862747 21 0.592234752328878 0.815530495342243 0.407765247671122 22 0.483801275897242 0.967602551794484 0.516198724102758 23 0.512190036439145 0.97561992712171 0.487809963560855 24 0.541176911949949 0.917646176100102 0.458823088050051 25 0.616463657710898 0.767072684578204 0.383536342289102 26 0.748611119696632 0.502777760606736 0.251388880303368 27 0.652223002538505 0.69555399492299 0.347776997461495 28 0.608403569228279 0.783192861543443 0.391596430771721 29 0.518015282828331 0.963969434343338 0.481984717171669 30 0.649028763274184 0.701942473451632 0.350971236725816 31 0.708113928431813 0.583772143136375 0.291886071568188 32 0.683400822163906 0.633198355672187 0.316599177836094 33 0.669954954154463 0.660090091691074 0.330045045845537 34 0.622517628640455 0.75496474271909 0.377482371359545 35 0.562026456742789 0.875947086514423 0.437973543257211 36 0.614844360348184 0.770311279303633 0.385155639651816 37 0.441861809500934 0.883723619001867 0.558138190499066 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 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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