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: Mon, 23 Nov 2009 13:50:02 -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/23/t1259009536k86ti3hm8f699ig.htm/, Retrieved Mon, 23 Nov 2009 21:52:27 +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/23/t1259009536k86ti3hm8f699ig.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:

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No (this computation is public)

User-defined keywords:

review 7

Dataseries X:

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6.5 0 6.3 6.1 6.2 6.3 6.6 0 6.5 6.3 6.1 6.2 6.5 0 6.6 6.5 6.3 6.1 6.2 0 6.5 6.6 6.5 6.3 6.2 0 6.2 6.5 6.6 6.5 5.9 0 6.2 6.2 6.5 6.6 6.1 0 5.9 6.2 6.2 6.5 6.1 0 6.1 5.9 6.2 6.2 6.1 0 6.1 6.1 5.9 6.2 6.1 0 6.1 6.1 6.1 5.9 6.1 0 6.1 6.1 6.1 6.1 6.4 0 6.1 6.1 6.1 6.1 6.7 0 6.4 6.1 6.1 6.1 6.9 0 6.7 6.4 6.1 6.1 7 0 6.9 6.7 6.4 6.1 7 0 7 6.9 6.7 6.4 6.8 0 7 7 6.9 6.7 6.4 0 6.8 7 7 6.9 5.9 0 6.4 6.8 7 7 5.5 0 5.9 6.4 6.8 7 5.5 0 5.5 5.9 6.4 6.8 5.6 0 5.5 5.5 5.9 6.4 5.8 0 5.6 5.5 5.5 5.9 5.9 0 5.8 5.6 5.5 5.5 6.1 0 5.9 5.8 5.6 5.5 6.1 0 6.1 5.9 5.8 5.6 6 0 6.1 6.1 5.9 5.8 6 0 6 6.1 6.1 5.9 5.9 0 6 6 6.1 6.1 5.5 0 5.9 6 6 6.1 5.6 0 5.5 5.9 6 6 5.4 0 5.6 5.5 5.9 6 5.2 0 5.4 5.6 5.5 5.9 5.2 0 5.2 5.4 5.6 5.5 5.2 0 5.2 5.2 5.4 5.6 5.5 0 5.2 5.2 5.2 5.4 5.8 1 5.5 5.2 5.2 5.2 5.8 1 5.8 5.5 5.2 5.2 5.5 1 5.8 5.8 5.5 5.2 5.3 1 5.5 5.8 5.8 5.5 5.1 1 5.3 5.5 5.8 5.8 5.2 1 5.1 5.3 5.5 5.8 5.8 1 5.2 5.1 5.3 5.5 5.8 1 5.8 5.2 5.1 5.3 5.5 1 5.8 5.8 5.2 5.1 5 1 5.5 5.8 5.8 5.2 4.9 1 5 etc...

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 x[t] = + 0.828266455762903 + 0.181690649604083y[t] -0.231079892362897`y-1`[t] -0.113984746512807`y-2`[t] + 0.403116044771066`y-3`[t] -0.451911443142585`y-4`[t] + 0.260083204498035M1[t] + 0.282413524108473M2[t] + 0.234756218660789M3[t] + 0.224037734894681M4[t] + 0.301228778766867M5[t] + 0.340721141705765M6[t] + 0.230155837767498M7[t] + 0.226055172545054M8[t] + 0.249926434867650M9[t] + 0.0489566955683181M10[t] + 0.0928502573330396M11[t] + 0.0198666404747040t + 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) 0.828266455762903 1.081117 0.7661 0.448599 0.2243 y 0.181690649604083 0.290964 0.6244 0.536273 0.268137 `y-1` -0.231079892362897 0.523453 -0.4415 0.661525 0.330763 `y-2` -0.113984746512807 0.549486 -0.2074 0.836836 0.418418 `y-3` 0.403116044771066 0.528222 0.7632 0.450342 0.225171 `y-4` -0.451911443142585 0.342055 -1.3212 0.194783 0.097391 M1 0.260083204498035 0.213724 1.2169 0.231555 0.115777 M2 0.282413524108473 0.234449 1.2046 0.236224 0.118112 M3 0.234756218660789 0.238767 0.9832 0.332069 0.166035 M4 0.224037734894681 0.241102 0.9292 0.358962 0.179481 M5 0.301228778766867 0.240233 1.2539 0.217959 0.108979 M6 0.340721141705765 0.25505 1.3359 0.189966 0.094983 M7 0.230155837767498 0.233398 0.9861 0.330661 0.16533 M8 0.226055172545054 0.269844 0.8377 0.407712 0.203856 M9 0.249926434867650 0.268449 0.931 0.358054 0.179027 M10 0.0489566955683181 0.234486 0.2088 0.835794 0.417897 M11 0.0928502573330396 0.226469 0.41 0.684242 0.342121 t 0.0198666404747040 0.004439 4.4755 7.4e-05 3.7e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.848135208984957 R-squared 0.719333332719956 Adjusted R-squared 0.586796295393269 F-TEST (value) 5.42741370434356 F-TEST (DF numerator) 17 F-TEST (DF denominator) 36 p-value 1.01676818082819e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.305868526919679 Sum Squared Residuals 3.36800000736053 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 -0.209627366669886 0.209627366669886 2 0 -0.21339472956232 0.21339472956232 3 0 -0.179445044766085 0.179445044766085 4 0 -0.22285364802801 0.22285364802801 5 0 -0.0951442054723797 0.0951442054723797 6 0 -0.141599721777526 0.141599721777526 7 0 -0.202379956728465 0.202379956728465 8 0 -0.0630611030521655 0.0630611030521655 9 0 -0.163054962988747 0.163054962988747 10 0 -0.127961419916386 0.127961419916386 11 0 -0.154583506305478 0.154583506305478 12 0 -0.173059928282589 0.173059928282589 13 0 0.092073143862506 -0.092073143862506 14 0 0.0670888422057528 -0.0670888422057528 15 0 0.0979906531980796 -0.0979906531980796 16 0 0.0465952518563678 -0.0465952518563678 17 0 0.0409661076425993 -0.0409661076425993 18 0 0.0237941455357358 -0.0237941455357358 19 0 -0.0877120807964054 0.0877120807964054 20 0 -0.0641117295534201 0.0641117295534201 21 0 0.0581863741655331 -0.0581863741655331 22 0 -0.0799472062220622 0.0799472062220622 23 0 0.0617524403647565 -0.0617524403647565 24 0 0.130088012600003 -0.130088012600003 25 0 0.440782653431814 -0.440782653431814 26 0 0.46079722503305 -0.46079722503305 27 0 0.341969861645691 -0.341969861645691 28 0 0.40965807223053 -0.40965807223053 29 0 0.409562877639777 -0.409562877639777 30 0 0.379042005970928 -0.379042005970928 31 0 0.455533983378472 -0.455533983378472 32 0 0.417136133601642 -0.417136133601642 33 0 0.343298136705256 -0.343298136705256 34 0 0.45228414738991 -0.45228414738991 35 0 0.413026945663426 -0.413026945663426 36 0 0.404309603360619 -0.404309603360619 37 1 0.75982496413423 0.24017503586577 38 1 0.69850253255666 0.301497467443339 39 1 0.702944062179934 0.297055937820066 40 1 0.730439437165126 0.269560562834874 41 1 0.735996961074847 0.264003038925153 42 1 0.761603143792678 0.238396856207322 43 1 0.834558054146398 0.165441945853602 44 1 0.710036699003943 0.289963300996057 45 1 0.761570452117958 0.238429547882042 46 1 0.755624478748539 0.244375521251461 47 1 0.679804120277295 0.320195879722705 48 1 0.638662312321966 0.361337687678034 49 1 0.916946605241336 0.0830533947586643 50 1 0.987006129766856 0.0129938702331438 51 1 1.03654046774238 -0.0365404677423810 52 1 1.03616088677599 -0.0361608867759864 53 1 0.908618259115157 0.0913817408848432 54 1 0.977160426478184 0.0228395735218164 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0 0 1 22 0 0 1 23 0 0 1 24 0 0 1 25 0 0 1 26 0 0 1 27 0 0 1 28 0 0 1 29 0 0 1 30 0 0 1 31 0 0 1 32 0 0 1 33 0 0 1 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 1 NOK 5% type I error level 13 1 NOK 10% type I error level 13 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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