WS 7 Multiple regression 4

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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 12:59:08 -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/t1258660817tbv5dr3pj5ui4fz.htm/, Retrieved Thu, 19 Nov 2009 21:00:29 +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/t1258660817tbv5dr3pj5ui4fz.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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Dataseries X:

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95,26 96,8 94,76 119,93 101,21 108,01 117,96 114,1 95,26 94,76 119,93 101,21 115,86 110,3 117,96 95,26 94,76 119,93 111,44 103,9 115,86 117,96 95,26 94,76 108,16 101,6 111,44 115,86 117,96 95,26 108,77 94,6 108,16 111,44 115,86 117,96 109,45 95,9 108,77 108,16 111,44 115,86 124,83 104,7 109,45 108,77 108,16 111,44 115,31 102,8 124,83 109,45 108,77 108,16 109,49 98,1 115,31 124,83 109,45 108,77 124,24 113,9 109,49 115,31 124,83 109,45 92,85 80,9 124,24 109,49 115,31 124,83 98,42 95,7 92,85 124,24 109,49 115,31 120,88 113,2 98,42 92,85 124,24 109,49 111,72 105,9 120,88 98,42 92,85 124,24 116,1 108,8 111,72 120,88 98,42 92,85 109,37 102,3 116,1 111,72 120,88 98,42 111,65 99 109,37 116,1 111,72 120,88 114,29 100,7 111,65 109,37 116,1 111,72 133,68 115,5 114,29 111,65 109,37 116,1 114,27 100,7 133,68 114,29 111,65 109,37 126,49 109,9 114,27 133,68 114,29 111,65 131 114,6 126,49 114,27 133,68 114,29 104 85,4 131 126,49 114,27 133,68 108,88 100,5 104 131 126,49 114,27 128,48 114,8 108,88 104 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 Y[t] = -40.0888737749896 + 0.965538000196312X[t] + 0.211997203187267Y1[t] + 0.314978135556808Y2[t] + 0.157411623308698Y3[t] -0.179123688240991Y4[t] -10.6311348674679M1[t] + 1.03583125266299M2[t] + 3.24681617767808M3[t] -8.72618456159211M4[t] -11.3837568394227M5[t] -2.30380200294361M6[t] + 0.542620183436238M7[t] + 3.56311254662019M8[t] -4.05010861645826M9[t] -4.49687150415468M10[t] -4.03469937535103M11[t] + 0.0118021665660321t + 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) -40.0888737749896 12.061746 -3.3236 0.001975 0.000987 X 0.965538000196312 0.086521 11.1596 0 0 Y1 0.211997203187267 0.075867 2.7943 0.008105 0.004053 Y2 0.314978135556808 0.068963 4.5673 5.1e-05 2.5e-05 Y3 0.157411623308698 0.090882 1.732 0.091377 0.045689 Y4 -0.179123688240991 0.09768 -1.8338 0.074529 0.037264 M1 -10.6311348674679 2.617157 -4.0621 0.000235 0.000117 M2 1.03583125266299 3.500092 0.2959 0.768884 0.384442 M3 3.24681617767808 3.868792 0.8392 0.406588 0.203294 M4 -8.72618456159211 3.687309 -2.3665 0.023155 0.011577 M5 -11.3837568394227 2.665673 -4.2705 0.000126 6.3e-05 M6 -2.30380200294361 2.500755 -0.9212 0.362736 0.181368 M7 0.542620183436238 2.583021 0.2101 0.834734 0.417367 M8 3.56311254662019 3.194155 1.1155 0.271637 0.135818 M9 -4.05010861645826 2.834299 -1.429 0.161184 0.080592 M10 -4.49687150415468 2.607262 -1.7247 0.092699 0.04635 M11 -4.03469937535103 2.832042 -1.4247 0.162417 0.081208 t 0.0118021665660321 0.053485 0.2207 0.826536 0.413268 Multiple Linear Regression - Regression Statistics Multiple R 0.98352786285997 R-squared 0.9673270570219 Adjusted R-squared 0.952710214110644 F-TEST (value) 66.1789322697735 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.49539822501776 Sum Squared Residuals 236.626467454028 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.26 97.2045355426287 -1.94453554262867 2 117.96 121.929896830728 -3.96989683072825 3 115.86 118.138219099141 -2.27821909914148 4 111.44 111.289635920307 0.150364079692696 5 108.16 108.308328690821 -0.148328690821096 6 108.77 104.157093374858 4.612906625142 7 109.45 107.047107507659 2.40289249234138 8 124.83 119.187847777566 5.6421522224342 9 115.31 113.910155485528 1.39984451447206 10 109.49 111.761090968019 -2.27109096801872 11 124.24 125.557336751923 -1.31733675192334 12 92.85 94.7813893063884 -1.93138930638843 13 98.42 97.2324761642042 1.18752383579579 14 120.88 120.466141510327 0.41385848967269 15 111.72 114.573161341898 -2.85316134189815 16 116.1 117.044012828888 -0.944012828887981 17 109.37 108.703339860618 0.666660139381755 18 111.65 109.096676011904 2.55332398809623 19 114.29 114.290101630533 -0.000101630532604924 20 133.68 131.046239349309 2.63376065069116 21 114.27 115.661426920568 -1.3914269205678 22 126.49 126.109140812171 0.380859187829363 23 131 130.177348759253 0.82265124074683 24 104 104.306712974902 -0.306712974902057 25 108.88 109.363991807859 -0.483991807859451 26 128.48 125.901125139701 2.57887486029903 27 132.44 130.399603652302 2.04039634769824 28 128.04 127.580056964679 0.459943035320896 29 116.35 116.935592592290 -0.585592592290121 30 120.93 123.137876233190 -2.20787623319043 31 118.59 121.207135823945 -2.6171358239449 32 133.1 137.168722113519 -4.06872211351877 33 121.05 122.458902245849 -1.40890224584852 34 127.62 125.940699883183 1.67930011681706 35 135.44 134.342951556277 1.09704844372256 36 114.88 113.771994195632 1.10800580436833 37 114.34 115.746557427993 -1.40655742799279 38 128.85 128.902978422081 -0.0529784220806831 39 138.9 138.953452723380 -0.0534527233804785 40 129.44 128.504543741499 0.935456258500719 41 114.96 116.557924393677 -1.59792439367745 42 127.98 128.914427432180 -0.934427432179746 43 127.03 128.710294744851 -1.68029474485127 44 128.75 132.160783041184 -3.41078304118390 45 137.91 136.509515348056 1.40048465194426 46 128.37 128.159068336628 0.210931663372300 47 135.9 136.502362932546 -0.602362932546049 48 122.19 121.059903523078 1.13009647692215 49 113.08 110.432439057315 2.64756094268512 50 136.2 135.169858097163 1.03014190283722 51 138 134.855563183278 3.14443681672186 52 115.24 115.841750544626 -0.601750544626329 53 110.95 109.284814462593 1.66518553740691 54 99.23 103.253926947868 -4.02392694786806 55 102.39 100.495360293013 1.8946397069874 56 112.67 113.466407718423 -0.796407718422687 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0886573984228738 0.177314796845748 0.911342601577126 22 0.473056023391612 0.946112046783224 0.526943976608388 23 0.40802895075594 0.81605790151188 0.59197104924406 24 0.313827954640074 0.627655909280147 0.686172045359926 25 0.337342893036547 0.674685786073094 0.662657106963453 26 0.362982319672024 0.725964639344048 0.637017680327976 27 0.430665555825249 0.861331111650498 0.569334444174751 28 0.320059522903959 0.640119045807918 0.679940477096041 29 0.271175288193983 0.542350576387965 0.728824711806017 30 0.711631622049653 0.576736755900694 0.288368377950347 31 0.765477187332251 0.469045625335499 0.234522812667749 32 0.829540749718275 0.34091850056345 0.170459250281725 33 0.712216000643809 0.575567998712382 0.287783999356191 34 0.589422072687887 0.821155854624226 0.410577927312113 35 0.517777370932639 0.964445258134721 0.482222629067361 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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