Model 5

*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 12:59:48 -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/t1258747290oklm4uczg9pex4p.htm/, Retrieved Fri, 20 Nov 2009 21:01:43 +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/t1258747290oklm4uczg9pex4p.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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20.3 18 13.2 15.7 12.6 12.8 23 20.3 13.2 15.7 8 20 12.8 20.3 13.2 0.9 20 8 12.8 20.3 3.6 15 0.9 8 12.8 14.1 17 3.6 0.9 8 21.7 16 14.1 3.6 0.9 24.5 15 21.7 14.1 3.6 18.9 10 24.5 21.7 14.1 13.9 13 18.9 24.5 21.7 11 10 13.9 18.9 24.5 5.8 19 11 13.9 18.9 15.5 21 5.8 11 13.9 22.4 17 15.5 5.8 11 31.7 16 22.4 15.5 5.8 30.3 17 31.7 22.4 15.5 31.4 14 30.3 31.7 22.4 20.2 18 31.4 30.3 31.7 19.7 17 20.2 31.4 30.3 10.8 14 19.7 20.2 31.4 13.2 15 10.8 19.7 20.2 15.1 16 13.2 10.8 19.7 15.6 11 15.1 13.2 10.8 15.5 15 15.6 15.1 13.2 12.7 13 15.5 15.6 15.1 10.9 17 12.7 15.5 15.6 10 16 10.9 12.7 15.5 9.1 9 10 10.9 12.7 10.3 17 9.1 10 10.9 16.9 15 10.3 9.1 10 22 12 16.9 10.3 9.1 27.6 12 22 16.9 10.3 28.9 12 27.6 22 16.9 31 12 28.9 27.6 22 32.9 4 31 28.9 27.6 38.1 7 32.9 31 28.9 28.8 4 38.1 32.9 31 29 3 28.8 38.1 32.9 21.8 3 29 28.8 38.1 28.8 0 21.8 29 28.8 25.6 5 28.8 21.8 29 28.2 3 25.6 28.8 21.8 20.2 4 28.2 25.6 28.8 17.9 3 20.2 28.2 25.6 16.3 10 17.9 20.2 28.2 13.2 4 16.3 17.9 20.2 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 4.44986041010845 -0.00197808566653005X[t] + 0.994282176708847`Yt-1`[t] + 0.147066157402592`Yt-2`[t] -0.382511912582321`Yt-3`[t] + 0.261349548161055M1[t] -0.168476823791646M2[t] -0.471950531563776M3[t] -0.510604588431602M4[t] + 0.146131731851114M5[t] + 0.88606344273659M6[t] + 1.08792158458782M7[t] + 0.0320781246262102M8[t] + 0.147371388525378M9[t] + 0.201264697862938M10[t] -0.309509853446752M11[t] -0.0185575755601159t + 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) 4.44986041010845 6.102328 0.7292 0.470124 0.235062 X -0.00197808566653005 0.228791 -0.0086 0.993145 0.496572 `Yt-1` 0.994282176708847 0.146636 6.7806 0 0 `Yt-2` 0.147066157402592 0.216018 0.6808 0.499916 0.249958 `Yt-3` -0.382511912582321 0.149498 -2.5586 0.014398 0.007199 M1 0.261349548161055 3.492971 0.0748 0.94073 0.470365 M2 -0.168476823791646 3.498967 -0.0482 0.961836 0.480918 M3 -0.471950531563776 3.495366 -0.135 0.893272 0.446636 M4 -0.510604588431602 3.535994 -0.1444 0.885908 0.442954 M5 0.146131731851114 3.498611 0.0418 0.966891 0.483446 M6 0.88606344273659 3.50557 0.2528 0.801749 0.400875 M7 1.08792158458782 3.509969 0.31 0.758207 0.379103 M8 0.0320781246262102 3.519304 0.0091 0.992773 0.496386 M9 0.147371388525378 3.532918 0.0417 0.966934 0.483467 M10 0.201264697862938 3.673779 0.0548 0.956583 0.478292 M11 -0.309509853446752 3.792425 -0.0816 0.935362 0.467681 t -0.0185575755601159 0.083933 -0.2211 0.826139 0.41307 Multiple Linear Regression - Regression Statistics Multiple R 0.897242589915076 R-squared 0.805044265157513 Adjusted R-squared 0.727061971220518 F-TEST (value) 10.3234237480618 F-TEST (DF numerator) 16 F-TEST (DF denominator) 40 p-value 1.33000888080659e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.18760048847671 Sum Squared Residuals 1076.44795312175 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 20.3 15.2708601459521 5.0291398540479 2 12.8 20.3185369022278 -7.51853690222775 3 8 14.5457730495929 -6.54577304959294 4 0.9 5.8971762091086 -4.9971762091086 5 3.6 1.64876371636601 1.95123628363399 6 14.1 5.84263102030894 8.25736897969105 7 21.7 19.5807857320310 2.11921426796903 8 24.5 26.5763198139180 -2.07631981391795 9 18.9 26.5682637395198 -7.66826373951976 10 13.9 18.5343797318297 -4.63437973182968 11 11 11.1449671417302 -0.144967141730218 12 5.8 9.94143425961047 -4.14143425961047 13 15.5 6.49607044843643 9.00392955156357 14 22.4 16.0446764856608 6.3553235143392 15 31.7 26.0007739795193 5.69922602048065 16 30.3 32.4927994388465 -2.19279943884652 17 31.4 30.4733004602024 0.926699539797574 18 20.2 28.5172192398622 -8.31721923986218 19 19.7 18.2638269634388 1.43617303656117 20 10.8 14.6303150298127 -3.83031502981268 21 13.2 10.0865616019972 3.11343839800283 22 15.1 11.3885636296174 3.71143637038260 23 15.6 16.5155728665759 -0.915572866575938 24 15.5 16.6571509990182 -1.15715099901824 25 12.7 16.1512313700762 -3.45123137007623 26 10.9 12.7049824130811 -1.80498241308110 27 10 10.2216872478704 -0.221687247870438 28 9.1 10.0897825279761 -0.989782527976076 29 10.3 10.3734445293143 -0.0734445293143178 30 16.9 12.5038146276851 4.39618537231489 31 22 19.7760519274614 2.22394807253859 32 27.6 24.2841123369131 3.31588766308688 33 28.9 28.1742869945316 0.725713005468367 34 31 28.3749492853152 2.62505071468475 35 32.9 27.9985537090286 4.90144629097136 36 38.1 29.9842813098509 8.11571869014908 37 28.8 34.8794255409795 -6.0794255409795 38 29 25.224166820328 3.77583317967199 39 21.8 21.7442147630654 0.0557852369346515 40 28.8 18.1208797338294 10.6791202661706 41 25.6 24.5737645713662 1.02623542863384 42 28.2 25.9009407849671 2.29905921503288 43 20.2 25.5192018332702 -5.31920183327018 44 17.9 18.0989315992544 -0.198931599254356 45 16.3 13.7239114495626 2.57608855043742 46 13.2 14.9021073532377 -1.70210735323766 47 8.1 11.9409062826652 -3.8409062826652 48 4.5 7.3171334315204 -2.81713343152039 49 -0.1 4.40241249455575 -4.50241249455575 50 0 0.80763737870233 -0.80763737870233 51 2.3 1.28755095995193 1.01244904004807 52 2.8 5.29936209023939 -2.49936209023940 53 2.9 6.73072672275109 -3.83072672275109 54 0.1 6.73539432717664 -6.63539432717664 55 3.5 3.96013354379861 -0.460133543798610 56 8.6 5.81032122010188 2.78967877989812 57 13.8 12.5469762143888 1.25302378561116 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.484179905285782 0.968359810571564 0.515820094714218 21 0.406743277817977 0.813486555635955 0.593256722182023 22 0.31176777280981 0.62353554561962 0.68823222719019 23 0.626222086499188 0.747555827001625 0.373777913500812 24 0.612751521969809 0.774496956060381 0.387248478030191 25 0.9192124125142 0.161575174971601 0.0807875874858007 26 0.900258895221135 0.199482209557731 0.0997411047788653 27 0.880673011989075 0.238653976021850 0.119326988010925 28 0.879737068877782 0.240525862244437 0.120262931122218 29 0.94930753646021 0.101384927079579 0.0506924635397893 30 0.90811199081415 0.183776018371702 0.091888009185851 31 0.874464250578052 0.251071498843895 0.125535749421948 32 0.806966135671783 0.386067728656435 0.193033864328218 33 0.711064463603532 0.577871072792937 0.288935536396468 34 0.841518140392014 0.316963719215971 0.158481859607986 35 0.763948456876766 0.472103086246469 0.236051543123234 36 0.85406889398904 0.29186221202192 0.14593110601096 37 0.753262453180023 0.493475093639953 0.246737546819977 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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