Multiple Regression analysis (4 time lags)

*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: Tue, 15 Dec 2009 12:30:45 -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/15/t1260905550gjx70eiyrgq84dj.htm/, Retrieved Tue, 15 Dec 2009 20:32:43 +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/Dec/15/t1260905550gjx70eiyrgq84dj.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)

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Dataseries X:

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113,08 96,90 96,33 106,46 95,10 96,33 123,38 97,00 95,05 109,87 112,70 96,84 95,74 102,90 96,92 123,06 97,40 97,44 123,39 111,40 97,78 120,28 87,40 97,69 115,33 96,80 96,67 110,40 114,10 98,29 114,49 110,30 98,20 132,03 103,90 98,71 123,16 101,60 98,54 118,82 94,60 98,20 128,32 95,90 100,80 112,24 104,70 101,33 104,53 102,80 101,88 132,57 98,10 101,85 122,52 113,90 102,04 131,80 80,90 102,22 124,55 95,70 102,63 120,96 113,20 102,65 122,60 105,90 102,54 145,52 108,80 102,37 118,57 102,30 102,68 134,25 99,00 102,76 136,70 100,70 102,82 121,37 115,50 103,31 111,63 100,70 103,23 134,42 109,90 103,60 137,65 114,60 103,95 137,86 85,40 103,93 119,77 100,50 104,25 130,69 114,80 104,38 128,28 116,50 104,36 147,45 112,90 104,32 128,42 102,00 104,58 136,90 106,00 104,68 143,95 105,30 104,92 135,64 118,80 105,46 122,48 106,10 105,23 136,83 109,30 105,58 153,04 117,20 105,34 142,71 92,50 105,28 123,46 104,20 105,70 144,37 112,50 105,67 146,15 122,40 105,71 147,61 113,30 106,1 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Uitvoer[t] = + 363.352795622603 + 0.921775814575904TIP[t] -3.46317522752666cons[t] -4.25013298896887M1[t] -5.0907676742516M2[t] + 5.11786220743184M3[t] -13.9124269008515M4[t] -22.1881699736302M5[t] + 3.53402423404762M6[t] -4.37096560255769M7[t] + 11.9907496437046M8[t] -10.6140628334390M9[t] -20.2941710232316M10[t] -19.5489939039977M11[t] + 1.07177313261062t + 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) 363.352795622603 175.09485 2.0752 0.043242 0.021621 TIP 0.921775814575904 0.295261 3.1219 0.003012 0.001506 cons -3.46317522752666 1.691119 -2.0479 0.045953 0.022976 M1 -4.25013298896887 6.839843 -0.6214 0.537231 0.268615 M2 -5.0907676742516 6.893627 -0.7385 0.463749 0.231874 M3 5.11786220743184 6.73564 0.7598 0.451004 0.225502 M4 -13.9124269008515 6.603993 -2.1067 0.04029 0.020145 M5 -22.1881699736302 6.781261 -3.272 0.00196 0.00098 M6 3.53402423404762 6.795058 0.5201 0.605345 0.302672 M7 -4.37096560255769 7.217354 -0.6056 0.547563 0.273781 M8 11.9907496437046 8.630667 1.3893 0.171017 0.085509 M9 -10.6140628334390 7.096831 -1.4956 0.14117 0.070585 M10 -20.2941710232316 7.083564 -2.865 0.006126 0.003063 M11 -19.5489939039977 7.012533 -2.7877 0.007534 0.003767 t 1.07177313261062 0.425616 2.5182 0.015113 0.007557 Multiple Linear Regression - Regression Statistics Multiple R 0.776726195507704 R-squared 0.603303582787871 Adjusted R-squared 0.489961749298692 F-TEST (value) 5.32286768455591 F-TEST (DF numerator) 14 F-TEST (DF denominator) 49 p-value 5.45203608637301e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.6353811503737 Sum Squared Residuals 5542.45527847249 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 113.08 115.886842531008 -2.8068425310083 2 106.46 114.458784512099 -7.99878451209865 3 123.38 131.923425865321 -8.5434258653211 4 109.87 122.237706521217 -12.3677065212173 5 95.74 105.723279580003 -9.98327958000328 6 123.06 125.646628821810 -2.58662882181037 7 123.39 130.540793944519 -7.15079394451928 8 120.28 126.163348544048 -5.88334854404793 9 115.33 116.827440588606 -1.49744058860558 10 110.4 118.555483254994 -8.15548325499351 11 114.49 117.181371181927 -2.69137118192711 12 132.03 130.136553639211 1.89344636078896 13 123.16 125.426849198008 -2.26684919800769 14 118.82 120.383036520663 -1.56303652066334 15 128.32 123.857492502337 4.46250749766319 16 112.24 112.175120824343 0.0648791756570806 17 104.53 101.315030461341 3.21496953865905 18 132.57 123.880546729948 8.68945327005155 19 122.52 130.953384603023 -8.43338460302296 20 131.8 117.344899559936 14.4551004400637 21 124.55 108.034240427841 16.5157595721593 22 120.96 115.487718621186 5.4722813788135 23 122.6 110.956654701655 11.6433452983451 24 145.52 134.839311389213 10.6806886107872 25 118.57 124.595824417578 -6.02582441757795 26 134.25 121.508048658603 12.7419513413968 27 136.7 134.147680044025 2.55231995597521 28 121.37 128.134490262587 -6.76449026258735 29 111.63 107.565292284898 4.06470771510198 30 134.42 141.5582222851 -7.13822228509996 31 137.65 137.845240579978 -0.195240579977643 32 137.86 128.432138677785 9.42786132221529 33 119.77 119.709698060539 0.0603019394606686 34 130.69 123.832544372214 6.85745562778567 35 128.28 127.285777013388 0.994222986611525 36 147.45 144.726678126625 2.7233218733754 37 128.42 130.600536332232 -2.18053633223205 38 136.9 134.172460515111 2.72753948488916 39 143.95 143.976458404595 -0.0264584045954077 40 135.64 136.591801302833 -0.951801302833051 41 122.48 118.477808819882 4.00219118011794 42 136.83 147.009347437179 -10.1793474371791 43 153.04 148.289321722940 4.75067827705957 44 142.71 143.16273799544 -0.452737995440148 45 123.46 130.959942085884 -7.499942085884 46 144.37 130.106241546508 14.2637584534922 47 146.15 140.910245353553 5.23975464644719 48 147.61 151.480528368308 -3.87052836830754 49 158.51 133.47980050972 25.0301994902800 50 147.4 141.807720806972 5.59227919302847 51 165.05 153.603951188589 11.4460488114109 52 154.64 129.901777073516 24.7382229264842 53 126.2 127.498588853876 -1.29858885387568 54 157.36 146.145254725962 11.2147452740378 55 154.15 143.121259149540 11.0287408504603 56 123.21 140.756875222791 -17.5468752227909 57 113.07 120.648678837130 -7.57867883713037 58 110.45 128.888012205098 -18.4380122050978 59 113.57 128.755951749477 -15.1859517494767 60 122.44 133.866928476644 -11.426928476644 61 114.93 126.680147011454 -11.7501470114540 62 111.85 123.349948986552 -11.4999489865524 63 126.04 135.930991995133 -9.89099199513284 64 121.34 126.059104015504 -4.7191040155036 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.00503860649539688 0.0100772129907938 0.994961393504603 19 0.0180586013285341 0.0361172026570683 0.981941398671466 20 0.00889422292250569 0.0177884458450114 0.991105777077494 21 0.00440926768896815 0.0088185353779363 0.995590732311032 22 0.00148766000787155 0.0029753200157431 0.998512339992129 23 0.000450160917219224 0.000900321834438447 0.99954983908278 24 0.000243328712372217 0.000486657424744435 0.999756671287628 25 0.00157924174012796 0.00315848348025592 0.998420758259872 26 0.00311670811365039 0.00623341622730079 0.99688329188635 27 0.00127069775086635 0.00254139550173269 0.998729302249134 28 0.00071908489700439 0.00143816979400878 0.999280915102996 29 0.000259223289937400 0.000518446579874799 0.999740776710063 30 0.000148984106938715 0.000297968213877431 0.999851015893061 31 7.3035433993487e-05 0.000146070867986974 0.999926964566006 32 3.89677351472816e-05 7.79354702945631e-05 0.999961032264853 33 8.52978689950896e-05 0.000170595737990179 0.999914702131005 34 4.14686043859618e-05 8.29372087719237e-05 0.999958531395614 35 1.61430712382156e-05 3.22861424764311e-05 0.999983856928762 36 6.65845344149485e-06 1.33169068829897e-05 0.999993341546559 37 3.70513943824805e-06 7.41027887649609e-06 0.999996294860562 38 1.42819484418818e-06 2.85638968837636e-06 0.999998571805156 39 4.06984092859831e-07 8.13968185719662e-07 0.999999593015907 40 2.34487063389262e-06 4.68974126778523e-06 0.999997655129366 41 7.90672203590424e-07 1.58134440718085e-06 0.999999209327796 42 0.000929344413405446 0.00185868882681089 0.999070655586595 43 0.0705576115275448 0.141115223055090 0.929442388472455 44 0.0543804183153715 0.108760836630743 0.945619581684628 45 0.49096916736119 0.98193833472238 0.50903083263881 46 0.341818377918636 0.683636755837272 0.658181622081364 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.758620689655172 NOK 5% type I error level 25 0.862068965517241 NOK 10% type I error level 25 0.862068965517241 NOK

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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