*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: Wed, 09 Dec 2009 07:20:25 -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/Dec/09/t1260368565cbg4lai22utevy5.htm/, Retrieved Wed, 09 Dec 2009 15:22:57 +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/Dec/09/t1260368565cbg4lai22utevy5.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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24 33 22 34 25 36 24 36 29 38 26 42 26 35 21 25 23 24 22 22 21 27 16 17 19 30 16 30 25 34 27 37 23 36 22 33 23 33 20 33 24 37 23 40 20 35 21 37 22 43 17 42 21 33 19 39 23 40 22 37 15 44 23 42 21 43 18 40 18 30 18 30 18 31 10 18 13 24 10 22 9 26 9 28 6 23 11 17 9 12 10 9 9 19 16 21 10 18 7 18 7 15 14 24 11 18 10 19 6 30 8 33 13 35 12 36 15 47 16 46 16 43

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 S.[t] = + 5.29372655439379 + 0.400869981642590E.S.[t] -0.35576928193259M1[t] -2.27843403304333M2[t] + 1.52156596695666M3[t] + 0.838782025700374M4[t] + 1.03878202570037M5[t] -0.241391970628143M6[t] -3.32243594859925M7[t] -0.71982600367148M8[t] + 0.6M9[t] -0.079304014685929M10[t] -1.36121797429962M11[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) 5.29372655439379 3.325294 1.592 0.117959 0.05898 E.S. 0.400869981642590 0.076001 5.2745 3e-06 2e-06 M1 -0.35576928193259 3.264875 -0.109 0.913682 0.456841 M2 -2.27843403304333 3.405549 -0.669 0.506678 0.253339 M3 1.52156596695666 3.405549 0.4468 0.657036 0.328518 M4 0.838782025700374 3.404463 0.2464 0.806441 0.40322 M5 1.03878202570037 3.404463 0.3051 0.761591 0.380796 M6 -0.241391970628143 3.404972 -0.0709 0.943777 0.471888 M7 -3.32243594859925 3.409447 -0.9745 0.334704 0.167352 M8 -0.71982600367148 3.402834 -0.2115 0.833364 0.416682 M9 0.6 3.4028 0.1763 0.86078 0.43039 M10 -0.079304014685929 3.403343 -0.0233 0.981506 0.490753 M11 -1.36121797429962 3.404463 -0.3998 0.691053 0.345526 Multiple Linear Regression - Regression Statistics Multiple R 0.62965823162227 R-squared 0.396469488649684 Adjusted R-squared 0.245586860812105 F-TEST (value) 2.62766823677324 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.00881546071620987 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.38029882265957 Sum Squared Residuals 1389.48554021337 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 18.1666666666667 5.83333333333329 2 22 16.6448718971985 5.35512810280152 3 25 21.2466118604837 3.75338813951632 4 24 20.5638279192274 3.43617208077261 5 29 21.5655678825126 7.43443211748743 6 26 21.8888738127544 4.11112618724559 7 26 16.0017399632852 9.99826003671482 8 21 14.5956500917870 6.40434990821295 9 23 15.5146061138159 7.48539388618406 10 22 14.0335621358448 7.96643786415516 11 21 14.7559980844441 6.24400191555591 12 16 12.1085162423178 3.89148375768218 13 19 16.9640567217389 2.03594327826111 14 16 15.0413919706281 0.958608029371852 15 25 20.4448718971985 4.5551281028015 16 27 20.96469790087 6.03530209913002 17 23 20.7638279192274 2.23617208077261 18 22 18.2810439779711 3.71895602202889 19 23 15.2 7.8 20 20 17.8026099449278 2.19739005507223 21 24 20.7259158751696 3.27408412483039 22 23 21.2492218054114 1.75077819458855 23 20 17.9629579375848 2.03704206241520 24 21 20.1259158751696 0.874084124830393 25 22 22.1753664830925 -0.175366483092550 26 17 19.8518317503392 -2.85183175033922 27 21 20.0440019155559 0.95599808444409 28 19 21.7664378641552 -2.76643786415516 29 23 22.3673078457978 0.63269215420225 30 22 19.8845239045415 2.11547609545854 31 15 19.6095697980685 -4.60956979806848 32 23 21.4104397797111 1.58956022028893 33 21 23.1311357650251 -2.13113576502514 34 18 21.2492218054114 -3.24922180541145 35 18 15.9586080293719 2.04139197062814 36 18 17.3198260036715 0.680173996328518 37 18 17.3649267033815 0.635073296618521 38 10 10.2309521909171 -0.230952190917076 39 13 16.4361720807726 -3.43617208077261 40 10 14.9516481762311 -4.95164817623114 41 9 16.7551281028015 -7.7551281028015 42 9 16.2766940697582 -7.27669406975816 43 6 11.1913001835741 -5.19130018357411 44 11 11.3886902386463 -0.388690238646338 45 9 10.7041663341049 -1.70416633410488 46 10 8.82225237449118 1.17774762550882 47 9 11.5490382313034 -2.54903823130338 48 16 13.7119961688882 2.28800383111182 49 10 12.1536169420278 -2.15361694202782 50 7 10.2309521909171 -3.23095219091708 51 7 12.8283422459893 -5.8283422459893 52 14 15.7533881395163 -1.75338813951632 53 11 13.5481682496608 -2.54816824966079 54 10 12.6688642349749 -2.66886423497486 55 6 13.9973900550722 -7.99739005507223 56 8 17.8026099449278 -9.80260994492777 57 13 19.9241759118844 -6.92417591188443 58 12 19.6457418788411 -7.64574187884109 59 15 22.7733977172959 -7.77339771729588 60 16 23.7337457099529 -7.73374570995291 61 16 22.1753664830926 -6.17536648309255 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0343445118019451 0.0686890236038901 0.965655488198055 17 0.0260192889578656 0.0520385779157311 0.973980711042134 18 0.0638090292559883 0.127618058511977 0.936190970744012 19 0.0545697298288899 0.109139459657780 0.94543027017111 20 0.102010460358928 0.204020920717856 0.897989539641072 21 0.101605476698440 0.203210953396880 0.89839452330156 22 0.0843411421510161 0.168682284302032 0.915658857848984 23 0.0629388088607004 0.125877617721401 0.9370611911393 24 0.0390410090077631 0.0780820180155262 0.960958990992237 25 0.0244545086943207 0.0489090173886414 0.97554549130568 26 0.0208573148729593 0.0417146297459187 0.97914268512704 27 0.0264345199960455 0.0528690399920911 0.973565480003954 28 0.0582830234172677 0.116566046834535 0.941716976582732 29 0.0745209097453136 0.149041819490627 0.925479090254686 30 0.107397316201122 0.214794632402244 0.892602683798878 31 0.338942778746247 0.677885557492493 0.661057221253753 32 0.552326697845922 0.895346604308156 0.447673302154078 33 0.664991082529348 0.670017834941304 0.335008917470652 34 0.722191795481039 0.555616409037922 0.277808204518961 35 0.828017922151875 0.343964155696251 0.171982077848125 36 0.782701180013068 0.434597639973865 0.217298819986932 37 0.85231620676747 0.295367586465062 0.147683793232531 38 0.883361289061262 0.233277421877477 0.116638710938738 39 0.951956653499143 0.0960866930017131 0.0480433465008566 40 0.972764913807646 0.0544701723847089 0.0272350861923545 41 0.980347872462071 0.0393042550758582 0.0196521275379291 42 0.974190727130412 0.0516185457391762 0.0258092728695881 43 0.951579382240186 0.0968412355196279 0.0484206177598139 44 0.965121969359513 0.0697560612809735 0.0348780306404868 45 0.903899332675134 0.192201334649732 0.0961006673248658 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 3 0.1 NOK 10% type I error level 12 0.4 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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