Revieuw ws7 yt-2

*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, 25 Nov 2009 13:47:03 -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/25/t1259182236h287cs9llczvrx5.htm/, Retrieved Wed, 25 Nov 2009 21:50:48 +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/25/t1259182236h287cs9llczvrx5.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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105.24 121.86 105.15 104.89 105.57 119.97 105.24 105.15 105.62 125.03 105.57 105.24 106.17 130.09 105.62 105.57 106.27 126.65 106.17 105.62 106.41 121.7 106.27 106.17 106.94 119.24 106.41 106.27 107.16 122.63 106.94 106.41 107.32 116.66 107.16 106.94 107.32 114.12 107.32 107.16 107.35 113.11 107.32 107.32 107.55 112.61 107.35 107.32 107.87 113.4 107.55 107.35 108.37 115.18 107.87 107.55 108.38 121.01 108.37 107.87 107.92 119.44 108.38 108.37 108.03 116.68 107.92 108.38 108.14 117.07 108.03 107.92 108.3 117.41 108.14 108.03 108.64 119.58 108.3 108.14 108.66 120.92 108.64 108.3 109.04 117.09 108.66 108.64 109.03 116.77 109.04 108.66 109.03 119.39 109.03 109.04 109.54 122.49 109.03 109.03 109.75 124.08 109.54 109.03 109.83 118.29 109.75 109.54 109.65 112.94 109.83 109.75 109.82 113.79 109.65 109.83 109.95 114.43 109.82 109.65 110.12 118.7 109.95 109.82 110.15 120.36 110.12 109.95 110.21 118.27 110.15 110.12 109.99 118.34 110.21 110.15 110.14 117.82 109.99 110.21 110.14 117.65 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 25.8088803582264 -0.00645300976920382X[t] + 0.856695033858175`Y(t-1)`[t] -0.091600614505897`Y(t-2)`[t] + 0.025943626539772t + 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) 25.8088803582264 8.764911 2.9446 0.004762 0.002381 X -0.00645300976920382 0.004573 -1.4111 0.163941 0.081971 `Y(t-1)` 0.856695033858175 0.133849 6.4005 0 0 `Y(t-2)` -0.091600614505897 0.133006 -0.6887 0.493964 0.246982 t 0.025943626539772 0.010394 2.4961 0.015644 0.007822 Multiple Linear Regression - Regression Statistics Multiple R 0.990686686541074 R-squared 0.981460110889733 Adjusted R-squared 0.980086785770454 F-TEST (value) 714.659695007225 F-TEST (DF numerator) 4 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.254644617699449 Sum Squared Residuals 3.50156959145812 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.24 105.521954568954 -0.281954568954383 2 105.57 105.613380777234 -0.0433807772338507 3 105.62 105.881137480209 -0.261137480209112 4 106.17 105.887035426223 0.282964573777319 5 106.27 106.401779644265 -0.131779644265217 6 106.41 106.49495483457 -0.0849548345701164 7 106.94 106.647550108432 0.292449891568315 8 107.16 107.092842313768 0.0671576862321354 9 107.32 107.297234990390 0.0227650096095419 10 107.32 107.45648833197 -0.136488331970016 11 107.35 107.474293400056 -0.124293400055739 12 107.55 107.529164382496 0.0208356175041438 13 107.87 107.718601119654 0.15139888034559 14 108.37 107.988880676738 0.381119323261558 15 108.38 108.376238576611 0.00376142338903572 16 107.92 108.375080071574 -0.455080071574005 17 108.03 108.023838283357 0.00616171664303265 18 108.14 108.183637972484 -0.0436379724838614 19 108.3 108.291547961831 0.00845203816914245 20 108.64 108.430483694993 0.209516305006890 21 108.66 108.724400501633 -0.0644005016329922 22 109.04 108.761048847334 0.278951152666041 23 109.03 109.112769537576 -0.0827695375758788 24 109.03 109.078431094670 -0.0484310946695092 25 109.54 109.085286397070 0.454713602930196 26 109.75 109.537884205344 0.212115794655779 27 109.83 109.734380402160 0.0956195978401118 28 109.65 109.844147104627 -0.194147104627307 29 109.82 109.703072517608 0.116927482391668 30 109.95 109.887012484263 0.0629875157372564 31 110.12 109.981200009024 0.138799990976416 32 110.15 110.130161715217 0.0198382847834003 33 110.21 110.179720878724 0.0302791212762367 34 109.99 110.253866478176 -0.263866478175993 35 110.14 110.089196725477 0.0508032745234049 36 110.14 110.264893753947 -0.124893753947160 37 110.81 110.273677193133 0.536322806866633 38 110.97 110.855279944614 0.114720055386418 39 110.99 110.932659048120 0.0573409518804941 40 109.73 110.919910274688 -1.18991027468797 41 109.81 109.871168216241 -0.0611682162409178 42 110.02 110.070674874038 -0.0506748740383596 43 110.18 110.249966439416 -0.0699664394156333 44 110.21 110.389744276270 -0.179744276269591 45 110.25 110.394661196951 -0.144661196951204 46 110.36 110.477743055194 -0.117743055193872 47 110.51 110.624910907282 -0.114910907281518 48 110.6 110.786705847681 -0.186705847681234 49 110.95 110.843811416344 0.106188583655988 50 111.18 111.133219126835 0.0467808731651101 51 111.19 111.272647378127 -0.082647378126744 52 111.69 111.295575738029 0.394424261970537 53 111.7 111.719654211001 -0.0196542110010731 54 111.83 111.659966907357 0.170033092642541 55 111.77 111.78165201988 -0.0116520198799481 56 111.73 111.705309685496 0.0246903145035372 57 112.01 111.715258506895 0.294741493104709 58 111.86 112.047399492355 -0.187399492354562 59 112.04 111.934806975395 0.105193024604581 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.184274453669256 0.368548907338511 0.815725546330744 9 0.0835849568438295 0.167169913687659 0.91641504315617 10 0.111486675150776 0.222973350301553 0.888513324849224 11 0.192097843920492 0.384195687840984 0.807902156079508 12 0.116507393048687 0.233014786097374 0.883492606951313 13 0.068797680517179 0.137595361034358 0.931202319482821 14 0.0624299891334213 0.124859978266843 0.937570010866579 15 0.066840026317669 0.133680052635338 0.93315997368233 16 0.366977524921881 0.733955049843761 0.633022475078119 17 0.289120238845550 0.578240477691101 0.71087976115445 18 0.291382818630397 0.582765637260795 0.708617181369603 19 0.227990519573219 0.455981039146438 0.772009480426781 20 0.171974255869414 0.343948511738828 0.828025744130586 21 0.144869911724774 0.289739823449548 0.855130088275226 22 0.120812095092519 0.241624190185039 0.87918790490748 23 0.104080870691649 0.208161741383298 0.895919129308351 24 0.0779969128042924 0.155993825608585 0.922003087195708 25 0.108919619516853 0.217839239033707 0.891080380483147 26 0.081320302172794 0.162640604345588 0.918679697827206 27 0.0575247153156285 0.115049430631257 0.942475284684371 28 0.0599999346813593 0.119999869362719 0.94000006531864 29 0.0419172578981239 0.0838345157962479 0.958082742101876 30 0.0287232043310471 0.0574464086620942 0.971276795668953 31 0.0211794305676769 0.0423588611353539 0.978820569432323 32 0.0157325721332159 0.0314651442664319 0.984267427866784 33 0.0113606814818117 0.0227213629636234 0.988639318518188 34 0.0148289960838574 0.0296579921677148 0.985171003916143 35 0.0097080096280005 0.019416019256001 0.990291990372 36 0.00651391693822851 0.0130278338764570 0.993486083061772 37 0.0538538156131778 0.107707631226356 0.946146184386822 38 0.095034255002518 0.190068510005036 0.904965744997482 39 0.773225530451908 0.453548939096184 0.226774469548092 40 0.98686420902436 0.0262715819512784 0.0131357909756392 41 0.985203245421067 0.0295935091578656 0.0147967545789328 42 0.97285209755451 0.0542958048909813 0.0271479024454906 43 0.95468958816622 0.0906208236675615 0.0453104118337808 44 0.927471299260276 0.145057401479448 0.0725287007397238 45 0.897197827670233 0.205604344659533 0.102802172329767 46 0.863879648231575 0.272240703536849 0.136120351768425 47 0.826797741386016 0.346404517227968 0.173202258613984 48 0.882794127250057 0.234411745499887 0.117205872749943 49 0.831477204459405 0.337045591081191 0.168522795540595 50 0.717028982729023 0.565942034541953 0.282971017270977 51 0.904062707680867 0.191874584638266 0.095937292319133 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 8 0.181818181818182 NOK 10% type I error level 12 0.272727272727273 NOK

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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