M4

*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: Thu, 19 Nov 2009 09:26:59 -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/19/t1258648079on0tefnuvde5zvr.htm/, Retrieved Thu, 19 Nov 2009 17:28:11 +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/19/t1258648079on0tefnuvde5zvr.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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23 2497,84 21 25 19 21 23 2645,64 23 21 25 19 19 2756,76 23 23 21 25 18 2849,27 19 23 23 21 19 2921,44 18 19 23 23 19 2981,85 19 18 19 23 22 3080,58 19 19 18 19 23 3106,22 22 19 19 18 20 3119,31 23 22 19 19 14 3061,26 20 23 22 19 14 3097,31 14 20 23 22 14 3161,69 14 14 20 23 15 3257,16 14 14 14 20 11 3277,01 15 14 14 14 17 3295,32 11 15 14 14 16 3363,99 17 11 15 14 20 3494,17 16 17 11 15 24 3667,03 20 16 17 11 23 3813,06 24 20 16 17 20 3917,96 23 24 20 16 21 3895,51 20 23 24 20 19 3801,06 21 20 23 24 23 3570,12 19 21 20 23 23 3701,61 23 19 21 20 23 3862,27 23 23 19 21 23 3970,1 23 23 23 19 27 4138,52 23 23 23 23 26 4199,75 27 23 23 23 17 4290,89 26 27 23 23 24 4443,91 17 26 27 23 26 4502,64 24 17 26 27 24 4356,98 26 24 17 26 27 4591,27 24 26 24 17 27 4696,96 27 24 26 24 26 4621,4 27 27 24 26 24 4562,84 26 27 27 24 23 4202,52 24 26 27 27 23 4296,49 23 24 26 27 24 4435,23 23 23 24 26 17 4105,18 24 23 23 24 21 4116,68 17 24 23 23 19 3844,49 21 17 24 23 22 3720,98 19 21 1 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 Consvertr[t] = -0.872484218315952 + 0.00413803755490541Aand[t] + 0.437427745519679Y1[t] -0.0161778421047462Y2[t] -0.0110721431993476Y3[t] + 0.00787373937551976Y4[t] -0.101399226156349t + 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) -0.872484218315952 1.951029 -0.4472 0.656668 0.328334 Aand 0.00413803755490541 0.000941 4.3982 5.7e-05 2.9e-05 Y1 0.437427745519679 0.138562 3.1569 0.002702 0.001351 Y2 -0.0161778421047462 0.145394 -0.1113 0.911848 0.455924 Y3 -0.0110721431993476 0.145564 -0.0761 0.939672 0.469836 Y4 0.00787373937551976 0.123182 0.0639 0.949289 0.474645 t -0.101399226156349 0.02836 -3.5755 0.000787 0.000393 Multiple Linear Regression - Regression Statistics Multiple R 0.924194193330778 R-squared 0.854134906986328 Adjusted R-squared 0.836631095824687 F-TEST (value) 48.7970819096901 F-TEST (DF numerator) 6 F-TEST (DF denominator) 50 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.83563052198185 Sum Squared Residuals 402.040022859754 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 23 18.0987866910656 4.90121330893445 2 23 19.4663759370354 3.53362406296457 3 19 19.8839707688212 -0.88397076882118 4 18 18.3620311708896 -0.362031170889643 5 19 18.2023052167212 0.797694783278835 6 19 18.8487789996785 0.151221000321536 7 22 19.1193275649104 2.88067243508955 8 23 20.4173649756460 2.58263502435396 9 20 20.7669006196644 -0.766900619664364 10 14 19.0636108051839 -5.06361080518393 11 14 16.5479039610053 -2.5479039610053 12 14 16.8510688142358 -2.8510688142358 13 15 17.1875396745158 -2.18753967451580 14 11 17.5584658030909 -6.55846580309088 15 17 15.7669452203814 1.23305477961861 16 16 18.6279107314581 -2.6279107314581 17 20 18.5828687482241 1.41713125177591 18 24 20.864731701294 3.13526829870601 19 23 23.1109242923927 -0.110924292392672 20 20 22.8893037796343 -2.88930377963433 21 21 21.3861066006207 -0.38610660062075 22 19 21.4223980999389 -2.42239809993893 23 23 19.4996698379311 3.50033016206886 24 23 21.6897544748316 1.31024552516839 25 23 22.2184790196016 0.78152098039841 26 23 22.5032483314423 0.49675166855774 27 27 23.1302723477852 3.86972765221484 28 26 25.0319561431944 0.968043856805617 29 17 24.8055585458534 -7.80555854585345 30 24 21.3724013859790 2.62759861402103 31 26 24.7641910037041 1.23580899629589 32 24 24.913431373025 -0.91343137302498 33 27 24.7259531335835 2.27404686641654 34 27 26.4395139066035 0.560486093396464 35 26 26.0148028016340 -0.0148028016340279 36 24 25.1846884423937 -1.18468844239366 37 23 22.7572150936457 0.242784906354258 38 23 22.650667338413 0.349332661586988 39 24 23.1538278317522 0.84617216824784 40 17 22.1194217205673 -5.11942172056727 41 21 18.9795641261743 2.02043587382568 42 19 19.6037161915609 -0.603716191560853 43 22 18.1370398293107 3.86296017068925 44 22 19.0881249861894 2.91187501381059 45 18 19.7500027184294 -1.75000271842936 46 16 17.6158811977398 -1.61588119773976 47 14 15.5002447049247 -1.50024470492471 48 12 12.6484322674582 -0.648432267458164 49 14 11.7548944452859 2.24510555471415 50 16 12.2166528015011 3.78334719849893 51 8 9.80053771834596 -1.80053771834596 52 3 5.37067713222995 -2.37067713222995 53 0 2.57775585359076 -2.57775585359076 54 5 1.52548486483280 3.4745151351672 55 1 3.26141518764749 -2.26141518764749 56 1 0.740131249371868 0.259868750628132 57 3 1.42877181705817 1.57122818294183 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0872217606610457 0.174443521322091 0.912778239338954 11 0.125006643493869 0.250013286987739 0.87499335650613 12 0.0883164471251433 0.176632894250287 0.911683552874857 13 0.104894203338286 0.209788406676572 0.895105796661714 14 0.555889623219017 0.888220753561966 0.444110376780983 15 0.65153280358854 0.696934392822919 0.348467196411459 16 0.620591686963095 0.75881662607381 0.379408313036905 17 0.699904308877153 0.600191382245694 0.300095691122847 18 0.768285147796566 0.463429704406867 0.231714852203434 19 0.695986582444638 0.608026835110723 0.304013417555362 20 0.663958078232683 0.672083843534634 0.336041921767317 21 0.695187917526052 0.609624164947896 0.304812082473948 22 0.729177366230462 0.541645267539076 0.270822633769538 23 0.842198656504536 0.315602686990928 0.157801343495464 24 0.79025407326371 0.419491853472579 0.209745926736290 25 0.725147219499511 0.549705561000978 0.274852780500489 26 0.652521697268629 0.694956605462741 0.347478302731371 27 0.763221967460548 0.473556065078903 0.236778032539452 28 0.766500277492533 0.466999445014934 0.233499722507467 29 0.967809131616808 0.0643817367663846 0.0321908683831923 30 0.968873916784251 0.0622521664314976 0.0311260832157488 31 0.95392564788637 0.0921487042272602 0.0460743521136301 32 0.938568775069846 0.122862449860308 0.0614312249301541 33 0.9205753711819 0.158849257636201 0.0794246288181007 34 0.881511066501582 0.236977866996837 0.118488933498418 35 0.828536162927729 0.342927674144542 0.171463837072271 36 0.771835551804006 0.456328896391988 0.228164448195994 37 0.70252706753904 0.59494586492192 0.29747293246096 38 0.61457471335284 0.77085057329432 0.38542528664716 39 0.517965952759574 0.964068094480852 0.482034047240426 40 0.762195616970236 0.475608766059528 0.237804383029764 41 0.692571948854967 0.614856102290066 0.307428051145033 42 0.686536695931744 0.626926608136511 0.313463304068256 43 0.613940444341006 0.772119111317988 0.386059555658994 44 0.90318490062956 0.193630198740880 0.0968150993704402 45 0.83368716331832 0.332625673363361 0.166312836681680 46 0.718576986141355 0.562846027717289 0.281423013858645 47 0.884132744767533 0.231734510464935 0.115867255232467 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 3 0.0789473684210526 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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