multiple lineair regression

*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, 26 Nov 2008 11:14:43 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/26/t1227723343sw88891rpdb6e90.htm/, Retrieved Wed, 26 Nov 2008 18:15:52 +0000

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/2008/Nov/26/t1227723343sw88891rpdb6e90.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

multiple lineair regression

Dataseries X:

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147768 0 137507 0 136919 0 136151 0 133001 0 125554 0 119647 0 114158 0 116193 0 152803 0 161761 0 160942 0 149470 0 139208 0 134588 0 130322 0 126611 0 122401 0 117352 0 112135 0 112879 0 148729 0 157230 0 157221 0 146681 1 136524 1 132111 1 125326 1 122716 1 116615 1 113719 1 110737 1 112093 1 143565 1 149946 1 149147 1 134339 1 122683 1 115614 1 116566 1 111272 1 104609 1 101802 1 94542 1 93051 1 124129 1 130374 1 123946 1 114971 1 105531 0 104919 0 104782 0 101281 0 94545 0 93248 0 84031 0 87486 0 115867 0 120327 0 117008 0 108811 0

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation jonger_dan_25[t] = + 124677.388888889 -2794.26888888890plan[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) 124677.388888889 3203.455608 38.9197 0 0 plan -2794.26888888890 5003.957625 -0.5584 0.578676 0.289338 Multiple Linear Regression - Regression Statistics Multiple R 0.0725076672708857 R-squared 0.00525736181306548 Adjusted R-squared -0.0116026829019673 F-TEST (value) 0.311823717073413 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.578676359639138 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19220.7336476126 Sum Squared Residuals 21796759515.1956 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 124677.388888888 23090.6111111116 2 137507 124677.388888889 12829.6111111111 3 136919 124677.388888889 12241.6111111111 4 136151 124677.388888889 11473.6111111111 5 133001 124677.388888889 8323.6111111111 6 125554 124677.388888889 876.611111111097 7 119647 124677.388888889 -5030.3888888889 8 114158 124677.388888889 -10519.3888888889 9 116193 124677.388888889 -8484.3888888889 10 152803 124677.388888889 28125.6111111111 11 161761 124677.388888889 37083.6111111111 12 160942 124677.388888889 36264.6111111111 13 149470 124677.388888889 24792.6111111111 14 139208 124677.388888889 14530.6111111111 15 134588 124677.388888889 9910.6111111111 16 130322 124677.388888889 5644.6111111111 17 126611 124677.388888889 1933.61111111110 18 122401 124677.388888889 -2276.38888888890 19 117352 124677.388888889 -7325.3888888889 20 112135 124677.388888889 -12542.3888888889 21 112879 124677.388888889 -11798.3888888889 22 148729 124677.388888889 24051.6111111111 23 157230 124677.388888889 32552.6111111111 24 157221 124677.388888889 32543.6111111111 25 146681 121883.12 24797.88 26 136524 121883.12 14640.88 27 132111 121883.12 10227.88 28 125326 121883.12 3442.88 29 122716 121883.12 832.879999999999 30 116615 121883.12 -5268.12 31 113719 121883.12 -8164.12 32 110737 121883.12 -11146.12 33 112093 121883.12 -9790.12 34 143565 121883.12 21681.88 35 149946 121883.12 28062.88 36 149147 121883.12 27263.88 37 134339 121883.12 12455.88 38 122683 121883.12 799.879999999999 39 115614 121883.12 -6269.12 40 116566 121883.12 -5317.12 41 111272 121883.12 -10611.12 42 104609 121883.12 -17274.12 43 101802 121883.12 -20081.12 44 94542 121883.12 -27341.12 45 93051 121883.12 -28832.12 46 124129 121883.12 2245.88 47 130374 121883.12 8490.88 48 123946 121883.12 2062.88 49 114971 121883.12 -6912.12 50 105531 124677.388888889 -19146.3888888889 51 104919 124677.388888889 -19758.3888888889 52 104782 124677.388888889 -19895.3888888889 53 101281 124677.388888889 -23396.3888888889 54 94545 124677.388888889 -30132.3888888889 55 93248 124677.388888889 -31429.3888888889 56 84031 124677.388888889 -40646.3888888889 57 87486 124677.388888889 -37191.3888888889 58 115867 124677.388888889 -8810.3888888889 59 120327 124677.388888889 -4350.3888888889 60 117008 124677.388888889 -7669.3888888889 61 108811 124677.388888889 -15866.3888888889 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0455838229184352 0.0911676458368704 0.954416177081565 6 0.0458016429460278 0.0916032858920557 0.954198357053972 7 0.061613693030854 0.123227386061708 0.938386306969146 8 0.0899354885025005 0.179870977005001 0.9100645114975 9 0.0795228936269567 0.159045787253913 0.920477106373043 10 0.132303427324545 0.264606854649089 0.867696572675455 11 0.288034193046992 0.576068386093985 0.711965806953008 12 0.423800825130471 0.847601650260943 0.576199174869529 13 0.411717368155438 0.823434736310877 0.588282631844562 14 0.345566062955903 0.691132125911806 0.654433937044097 15 0.281707130770486 0.563414261540972 0.718292869229514 16 0.229391079445924 0.458782158891848 0.770608920554076 17 0.191091371240030 0.382182742480060 0.80890862875997 18 0.168420339694245 0.336840679388491 0.831579660305755 19 0.164554415141863 0.329108830283726 0.835445584858137 20 0.181596466476212 0.363192932952425 0.818403533523788 21 0.183721555061797 0.367443110123593 0.816278444938203 22 0.229676023625267 0.459352047250533 0.770323976374733 23 0.431314118684755 0.86262823736951 0.568685881315245 24 0.741411920969074 0.517176158061851 0.258588079030926 25 0.754591326995404 0.490817346009191 0.245408673004596 26 0.732386630195755 0.535226739608489 0.267613369804245 27 0.696832988902224 0.606334022195553 0.303167011097776 28 0.653209810617888 0.693580378764223 0.346790189382112 29 0.602861730766518 0.794276538466965 0.397138269233482 30 0.564237093630211 0.871525812739577 0.435762906369788 31 0.530105598126245 0.93978880374751 0.469894401873755 32 0.506574587527688 0.986850824944625 0.493425412472312 33 0.466120050028357 0.932240100056714 0.533879949971643 34 0.537795391151455 0.92440921769709 0.462204608848545 35 0.723250375192515 0.553499249614971 0.276749624807485 36 0.888784084720618 0.222431830558765 0.111215915279382 37 0.91090261576632 0.178194768467359 0.0890973842336795 38 0.893465859493868 0.213068281012265 0.106534140506132 39 0.865487465144708 0.269025069710584 0.134512534855292 40 0.83141985094482 0.337160298110358 0.168580149055179 41 0.79395704188135 0.412085916237298 0.206042958118649 42 0.77709373158605 0.445812536827899 0.222906268413950 43 0.778212237633306 0.443575524733388 0.221787762366694 44 0.862321004622197 0.275357990755607 0.137678995377803 45 0.961865192767544 0.076269614464912 0.038134807232456 46 0.937103792262132 0.125792415475737 0.0628962077378683 47 0.917344377566124 0.165311244867752 0.082655622433876 48 0.880903506640383 0.238192986719234 0.119096493359617 49 0.82167620489699 0.356647590206021 0.178323795103011 50 0.780851093416114 0.438297813167772 0.219148906583886 51 0.725085693705484 0.549828612589032 0.274914306294516 52 0.652111962234644 0.695776075530712 0.347888037765356 53 0.567392596217458 0.865214807565084 0.432607403782542 54 0.509563869679739 0.980872260640522 0.490436130320261 55 0.454280241478619 0.908560482957239 0.545719758521381 56 0.596342073710985 0.80731585257803 0.403657926289015 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 0.0576923076923077 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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