DSHW-WS7-MultipleRegression

*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 06:19:23 -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/t1258723575peuqajrf1wsv0d7.htm/, Retrieved Fri, 20 Nov 2009 14:26:27 +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/t1258723575peuqajrf1wsv0d7.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:

SDHW, DSHW

Dataseries X:

» Textbox « » Textfile « » CSV «

1.4 0.0 1.6 0.0 1.7 0.0 2.0 0.0 2.0 0.0 2.1 0.0 2.5 0.0 2.5 0.0 2.6 0.0 2.7 0.0 3.7 0.0 4.0 0.0 5.0 0.0 5.1 0.0 5.1 0.0 5.0 0.0 5.1 0.0 4.7 0.0 4.5 0.0 4.5 0.0 4.6 0.0 4.6 0.0 4.6 0.0 4.6 0.0 5.3 0.0 5.4 0.0 5.3 0.0 5.2 0.0 5.0 0.0 4.2 0.0 4.3 0.0 4.3 0.0 4.3 0.0 4.0 0.0 4.0 0.0 4.1 0.0 4.4 0.0 3.6 0.0 3.7 0.0 3.8 0.0 3.3 0.0 3.3 0.0 3.3 0.0 3.5 0.0 3.3 1.0 3.3 1.0 3.4 1.0 3.4 1.0 5.2 1.0 5.3 1.0 4.8 1.0 5.0 1.0 4.6 1.0 4.6 1.0 3.5 1.0 3.5 1.0

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation IndGez[t] = + 3.95159574468085 + 0.293617021276596InvlCrisis[t] + 0.249680851063827M1[t] + 0.189680851063829M2[t] + 0.109680851063829M3[t] + 0.189680851063830M4[t] -0.0103191489361709M5[t] -0.230319148936171M6[t] -0.390319148936171M7[t] -0.350319148936171M8[t] -0.325000000000001M9[t] -0.375000000000001M10[t] -0.100000000000001M11[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) 3.95159574468085 0.596642 6.6231 0 0 InvlCrisis 0.293617021276596 0.384132 0.7644 0.448824 0.224412 M1 0.249680851063827 0.790276 0.3159 0.753575 0.376788 M2 0.189680851063829 0.790276 0.24 0.811456 0.405728 M3 0.109680851063829 0.790276 0.1388 0.890266 0.445133 M4 0.189680851063830 0.790276 0.24 0.811456 0.405728 M5 -0.0103191489361709 0.790276 -0.0131 0.989642 0.494821 M6 -0.230319148936171 0.790276 -0.2914 0.772115 0.386058 M7 -0.390319148936171 0.790276 -0.4939 0.623889 0.311944 M8 -0.350319148936171 0.790276 -0.4433 0.65978 0.32989 M9 -0.325000000000001 0.832778 -0.3903 0.698271 0.349135 M10 -0.375000000000001 0.832778 -0.4503 0.654756 0.327378 M11 -0.100000000000001 0.832778 -0.1201 0.904979 0.45249 Multiple Linear Regression - Regression Statistics Multiple R 0.244918091516137 R-squared 0.0599848715519067 Adjusted R-squared -0.202344931735933 F-TEST (value) 0.228662053644315 F-TEST (DF numerator) 12 F-TEST (DF denominator) 43 p-value 0.995819144228298 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.17772560689915 Sum Squared Residuals 59.6426170212766 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.4 4.20127659574469 -2.80127659574469 2 1.6 4.14127659574468 -2.54127659574468 3 1.7 4.06127659574468 -2.36127659574468 4 2 4.14127659574468 -2.14127659574468 5 2 3.94127659574468 -1.94127659574468 6 2.1 3.72127659574468 -1.62127659574468 7 2.5 3.56127659574468 -1.06127659574468 8 2.5 3.60127659574468 -1.10127659574468 9 2.6 3.62659574468085 -1.02659574468085 10 2.7 3.57659574468085 -0.87659574468085 11 3.7 3.85159574468085 -0.151595744680851 12 4 3.95159574468085 0.0484042553191475 13 5 4.20127659574468 0.798723404255322 14 5.1 4.14127659574468 0.95872340425532 15 5.1 4.06127659574468 1.03872340425532 16 5 4.14127659574468 0.858723404255319 17 5.1 3.94127659574468 1.15872340425532 18 4.7 3.72127659574468 0.97872340425532 19 4.5 3.56127659574468 0.93872340425532 20 4.5 3.60127659574468 0.898723404255319 21 4.6 3.62659574468085 0.97340425531915 22 4.6 3.57659574468085 1.02340425531915 23 4.6 3.85159574468085 0.748404255319149 24 4.6 3.95159574468085 0.648404255319148 25 5.3 4.20127659574468 1.09872340425532 26 5.4 4.14127659574468 1.25872340425532 27 5.3 4.06127659574468 1.23872340425532 28 5.2 4.14127659574468 1.05872340425532 29 5 3.94127659574468 1.05872340425532 30 4.2 3.72127659574468 0.478723404255319 31 4.3 3.56127659574468 0.73872340425532 32 4.3 3.60127659574468 0.698723404255319 33 4.3 3.62659574468085 0.67340425531915 34 4 3.57659574468085 0.423404255319150 35 4 3.85159574468085 0.148404255319149 36 4.1 3.95159574468085 0.148404255319148 37 4.4 4.20127659574468 0.198723404255322 38 3.6 4.14127659574468 -0.54127659574468 39 3.7 4.06127659574468 -0.361276595744681 40 3.8 4.14127659574468 -0.341276595744681 41 3.3 3.94127659574468 -0.641276595744681 42 3.3 3.72127659574468 -0.421276595744681 43 3.3 3.56127659574468 -0.261276595744681 44 3.5 3.60127659574468 -0.101276595744681 45 3.3 3.92021276595745 -0.620212765957447 46 3.3 3.87021276595745 -0.570212765957447 47 3.4 4.14521276595745 -0.745212765957447 48 3.4 4.24521276595745 -0.845212765957448 49 5.2 4.49489361702127 0.705106382978726 50 5.3 4.43489361702128 0.865106382978723 51 4.8 4.35489361702128 0.445106382978723 52 5 4.43489361702128 0.565106382978723 53 4.6 4.23489361702128 0.365106382978723 54 4.6 4.01489361702128 0.585106382978723 55 3.5 3.85489361702128 -0.354893617021277 56 3.5 3.89489361702128 -0.394893617021277 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.999996044996917 7.91000616585657e-06 3.95500308292829e-06 17 0.999997222325781 5.55534843787163e-06 2.77767421893581e-06 18 0.99999636585489 7.2682902196604e-06 3.6341451098302e-06 19 0.999993725270836 1.254945832706e-05 6.27472916353e-06 20 0.999989000078352 2.19998432958388e-05 1.09999216479194e-05 21 0.999981275808219 3.7448383562669e-05 1.87241917813345e-05 22 0.999971286332285 5.74273354291272e-05 2.87136677145636e-05 23 0.999942536785366 0.000114926429267620 5.74632146338098e-05 24 0.999882698585769 0.000234602828462059 0.000117301414231030 25 0.99981690200314 0.000366195993722135 0.000183097996861068 26 0.999783637591957 0.00043272481608552 0.00021636240804276 27 0.999759548784868 0.000480902430263287 0.000240451215131643 28 0.99964250083027 0.000714998339462038 0.000357499169731019 29 0.999584769297865 0.000830461404269521 0.000415230702134761 30 0.998987787565668 0.00202442486866349 0.00101221243433175 31 0.998559895599478 0.00288020880104458 0.00144010440052229 32 0.9978390540135 0.00432189197299845 0.00216094598649923 33 0.997842188685963 0.00431562262807489 0.00215781131403745 34 0.997466367607502 0.00506726478499705 0.00253363239249852 35 0.99745640935416 0.00508718129167849 0.00254359064583925 36 0.999157415740752 0.00168516851849658 0.000842584259248291 37 0.99685664791349 0.00628670417301829 0.00314335208650915 38 0.994471660095292 0.0110566798094169 0.00552833990470844 39 0.980923252243788 0.0381534955124236 0.0190767477562118 40 0.945326351371421 0.109347297257157 0.0546736486285786 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.88 NOK 5% type I error level 24 0.96 NOK 10% type I error level 24 0.96 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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