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, 17 Dec 2008 02:54:45 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/17/t1229507789tzsaecpbh6qeoal.htm/, Retrieved Wed, 17 Dec 2008 10:56:41 +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/2008/Dec/17/t1229507789tzsaecpbh6qeoal.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

multiple lineair regression

Dataseries X:

» Textbox « » Textfile « » CSV «

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 0 136524 0 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 1 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation jonger_dan_25[t] = + 126109.729729730 -6551.22972972975plan[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) 126109.729729730 3122.713636 40.3847 0 0 plan -6551.22972972975 4978.419125 -1.3159 0.193289 0.096645 Multiple Linear Regression - Regression Statistics Multiple R 0.168858837431560 R-squared 0.0285133069787379 Adjusted R-squared 0.0120474308258351 F-TEST (value) 1.73166047855348 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.193289166757992 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18994.7254977231 Sum Squared Residuals 21287176207.2973 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 126109.729729729 21658.2702702708 2 137507 126109.729729730 11397.2702702703 3 136919 126109.729729730 10809.2702702703 4 136151 126109.729729730 10041.2702702703 5 133001 126109.729729730 6891.27027027026 6 125554 126109.729729730 -555.729729729742 7 119647 126109.729729730 -6462.72972972974 8 114158 126109.729729730 -11951.7297297297 9 116193 126109.729729730 -9916.72972972974 10 152803 126109.729729730 26693.2702702703 11 161761 126109.729729730 35651.2702702703 12 160942 126109.729729730 34832.2702702703 13 149470 126109.729729730 23360.2702702703 14 139208 126109.729729730 13098.2702702703 15 134588 126109.729729730 8478.27027027026 16 130322 126109.729729730 4212.27027027026 17 126611 126109.729729730 501.270270270258 18 122401 126109.729729730 -3708.72972972974 19 117352 126109.729729730 -8757.72972972974 20 112135 126109.729729730 -13974.7297297297 21 112879 126109.729729730 -13230.7297297297 22 148729 126109.729729730 22619.2702702703 23 157230 126109.729729730 31120.2702702703 24 157221 126109.729729730 31111.2702702703 25 146681 126109.729729730 20571.2702702703 26 136524 126109.729729730 10414.2702702703 27 132111 119558.5 12552.5 28 125326 119558.5 5767.5 29 122716 119558.5 3157.5 30 116615 119558.5 -2943.5 31 113719 119558.5 -5839.5 32 110737 119558.5 -8821.5 33 112093 119558.5 -7465.5 34 143565 119558.5 24006.5 35 149946 119558.5 30387.5 36 149147 119558.5 29588.5 37 134339 119558.5 14780.5 38 122683 119558.5 3124.5 39 115614 119558.5 -3944.5 40 116566 119558.5 -2992.5 41 111272 119558.5 -8286.5 42 104609 119558.5 -14949.5 43 101802 119558.5 -17756.5 44 94542 119558.5 -25016.5 45 93051 119558.5 -26507.5 46 124129 119558.5 4570.5 47 130374 119558.5 10815.5 48 123946 119558.5 4387.5 49 114971 119558.5 -4587.5 50 105531 119558.5 -14027.5 51 104919 126109.729729730 -21190.7297297297 52 104782 126109.729729730 -21327.7297297297 53 101281 126109.729729730 -24828.7297297297 54 94545 126109.729729730 -31564.7297297297 55 93248 126109.729729730 -32861.7297297297 56 84031 126109.729729730 -42078.7297297297 57 87486 126109.729729730 -38623.7297297297 58 115867 126109.729729730 -10242.7297297297 59 120327 126109.729729730 -5782.72972972974 60 117008 126109.729729730 -9101.72972972974 61 108811 126109.729729730 -17298.7297297297 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0465018471549714 0.0930036943099429 0.953498152845029 6 0.0469397780311425 0.093879556062285 0.953060221968858 7 0.0634686446416611 0.126937289283322 0.936531355358339 8 0.0932356561556779 0.186471312311356 0.906764343844322 9 0.0831223568296733 0.166244713659347 0.916877643170327 10 0.136458504628644 0.272917009257287 0.863541495371356 11 0.29055856984568 0.58111713969136 0.70944143015432 12 0.41866344821075 0.8373268964215 0.58133655178925 13 0.398567481484710 0.797134962969421 0.60143251851529 14 0.327039980009587 0.654079960019174 0.672960019990413 15 0.259723227765344 0.519446455530689 0.740276772234656 16 0.205757955377884 0.411515910755768 0.794242044622116 17 0.166911971528881 0.333823943057761 0.83308802847112 18 0.144045300960956 0.288090601921913 0.855954699039044 19 0.139460539803109 0.278921079606219 0.86053946019689 20 0.154924953262942 0.309849906525885 0.845075046737058 21 0.157063610838631 0.314127221677263 0.842936389161369 22 0.180775704109908 0.361551408219815 0.819224295890092 23 0.312989004907910 0.625978009815819 0.68701099509209 24 0.525797110978841 0.948405778042318 0.474202889021159 25 0.652439948254951 0.695120103490098 0.347560051745049 26 0.716368582037276 0.567262835925448 0.283631417962724 27 0.67197592856595 0.6560481428681 0.32802407143405 28 0.610713527275129 0.778572945449743 0.389286472724872 29 0.542924273933248 0.914151452133503 0.457075726066752 30 0.480829865289709 0.961659730579419 0.519170134710291 31 0.424331438082392 0.848662876164785 0.575668561917608 32 0.379171666208178 0.758343332416356 0.620828333791822 33 0.325642997371789 0.651285994743579 0.67435700262821 34 0.429971440853987 0.859942881707974 0.570028559146013 35 0.658289391955912 0.683421216088176 0.341710608044088 36 0.86338392430344 0.273232151393120 0.136616075696560 37 0.893385672054604 0.213228655890791 0.106614327945396 38 0.874046568489522 0.251906863020957 0.125953431510478 39 0.840763019068399 0.318473961863203 0.159236980931601 40 0.801589114446064 0.396821771107872 0.198410885553936 41 0.756878969326076 0.486242061347848 0.243121030673924 42 0.731711647192354 0.536576705615291 0.268288352807646 43 0.723643384045763 0.552713231908474 0.276356615954237 44 0.802937333278919 0.394125333442162 0.197062666721081 45 0.9115296255777 0.176940748844599 0.0884703744222994 46 0.872984114937754 0.254031770124492 0.127015885062246 47 0.86805792289709 0.263884154205819 0.131942077102910 48 0.844611177514244 0.310777644971513 0.155388822485756 49 0.790903960416466 0.418192079167067 0.209096039583534 50 0.715634832818526 0.568730334362948 0.284365167181474 51 0.665111417612067 0.669777164775866 0.334888582387933 52 0.597446900819727 0.805106198360546 0.402553099180273 53 0.520394515352877 0.959210969294246 0.479605484647123 54 0.473253948955519 0.946507897911038 0.526746051044481 55 0.427391302290759 0.854782604581518 0.572608697709241 56 0.580712145161579 0.838575709676843 0.419287854838421 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 2 0.0384615384615385 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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