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 10:36:14 -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/t1227721027dtz5jblvhraoopt.htm/, Retrieved Wed, 26 Nov 2008 17:37:17 +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/t1227721027dtz5jblvhraoopt.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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User-defined keywords:

multiple lineair regression

Dataseries X:

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159129 0 157928 0 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 0 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 1 104782 0 101281 0 94545 0 93248 0 84031 0 87486 0 115867 0 120327 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation jonger_dan_25[t] = + 129310.540540541 -10885.0405405405plan[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) 129310.540540541 3191.950521 40.5114 0 0 plan -10885.0405405405 5088.800759 -2.139 0.036583 0.018292 Multiple Linear Regression - Regression Statistics Multiple R 0.268268726654801 R-squared 0.0719681097009885 Adjusted R-squared 0.056238755628124 F-TEST (value) 4.57540146706621 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.0365832365930456 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19415.8770288601 Sum Squared Residuals 22241600567.1892 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 159129 129310.54054054 29818.4594594599 2 157928 129310.540540541 28617.4594594594 3 147768 129310.540540541 18457.4594594594 4 137507 129310.540540541 8196.45945945945 5 136919 129310.540540541 7608.45945945945 6 136151 129310.540540541 6840.45945945945 7 133001 129310.540540541 3690.45945945945 8 125554 129310.540540541 -3756.54054054055 9 119647 129310.540540541 -9663.54054054055 10 114158 129310.540540541 -15152.5405405406 11 116193 129310.540540541 -13117.5405405406 12 152803 129310.540540541 23492.4594594594 13 161761 129310.540540541 32450.4594594594 14 160942 129310.540540541 31631.4594594594 15 149470 129310.540540541 20159.4594594594 16 139208 129310.540540541 9897.45945945945 17 134588 129310.540540541 5277.45945945945 18 130322 129310.540540541 1011.45945945945 19 126611 129310.540540541 -2699.54054054055 20 122401 129310.540540541 -6909.54054054055 21 117352 129310.540540541 -11958.5405405406 22 112135 129310.540540541 -17175.5405405406 23 112879 129310.540540541 -16431.5405405406 24 148729 129310.540540541 19418.4594594594 25 157230 129310.540540541 27919.4594594594 26 157221 129310.540540541 27910.4594594594 27 146681 129310.540540541 17370.4594594594 28 136524 129310.540540541 7213.45945945945 29 132111 129310.540540541 2800.45945945945 30 125326 118425.5 6900.5 31 122716 118425.5 4290.5 32 116615 118425.5 -1810.50000000000 33 113719 118425.5 -4706.5 34 110737 118425.5 -7688.5 35 112093 118425.5 -6332.5 36 143565 118425.5 25139.5 37 149946 118425.5 31520.5 38 149147 118425.5 30721.5 39 134339 118425.5 15913.5 40 122683 118425.5 4257.5 41 115614 118425.5 -2811.500 42 116566 118425.5 -1859.50000000000 43 111272 118425.5 -7153.5 44 104609 118425.5 -13816.5 45 101802 118425.5 -16623.5 46 94542 118425.5 -23883.5 47 93051 118425.5 -25374.5 48 124129 118425.5 5703.5 49 130374 118425.5 11948.5 50 123946 118425.5 5520.5 51 114971 118425.5 -3454.5 52 105531 118425.5 -12894.5 53 104919 118425.5 -13506.5 54 104782 129310.540540541 -24528.5405405406 55 101281 129310.540540541 -28029.5405405406 56 94545 129310.540540541 -34765.5405405406 57 93248 129310.540540541 -36062.5405405406 58 84031 129310.540540541 -45279.5405405406 59 87486 129310.540540541 -41824.5405405406 60 115867 129310.540540541 -13443.5405405406 61 120327 129310.540540541 -8983.54054054055 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.256296789245774 0.512593578491548 0.743703210754226 6 0.180109083985554 0.360218167971108 0.819890916014446 7 0.137618063218695 0.275236126437390 0.862381936781305 8 0.149666182334560 0.299332364669119 0.85033381766544 9 0.189719944113815 0.379439888227629 0.810280055886185 10 0.254558387096164 0.509116774192328 0.745441612903836 11 0.260823993389608 0.521647986779217 0.739176006610392 12 0.261330173031195 0.52266034606239 0.738669826968805 13 0.354787262868217 0.709574525736434 0.645212737131783 14 0.432698525163227 0.865397050326454 0.567301474836773 15 0.399128506356798 0.798257012713595 0.600871493643202 16 0.331066033964024 0.662132067928047 0.668933966035976 17 0.269936731944140 0.539873463888281 0.73006326805586 18 0.222203782800785 0.444407565601569 0.777796217199215 19 0.188409058366766 0.376818116733532 0.811590941633234 20 0.169814853814950 0.339629707629899 0.83018514618505 21 0.169878477132366 0.339756954264732 0.830121522867634 22 0.191593582817062 0.383187165634125 0.808406417182938 23 0.198812024244364 0.397624048488727 0.801187975755636 24 0.208255262262127 0.416510524524255 0.791744737737873 25 0.311575296346567 0.623150592693134 0.688424703653433 26 0.480498811997813 0.960997623995625 0.519501188002187 27 0.580827681263508 0.838344637472983 0.419172318736492 28 0.631796002368841 0.736407995262317 0.368203997631159 29 0.691775581091487 0.616448837817026 0.308224418908513 30 0.629676917451865 0.740646165096271 0.370323082548135 31 0.560079508170101 0.879840983659798 0.439920491829899 32 0.490139904095536 0.980279808191072 0.509860095904464 33 0.424513573458288 0.849027146916576 0.575486426541712 34 0.369148692579006 0.738297385158011 0.630851307420994 35 0.309541095736867 0.619082191473734 0.690458904263133 36 0.42185040395696 0.84370080791392 0.57814959604304 37 0.658036659481447 0.683926681037107 0.341963340518553 38 0.869945607382656 0.260108785234688 0.130054392617344 39 0.903522989626348 0.192954020747303 0.0964770103736516 40 0.886569592585354 0.226860814829292 0.113430407414646 41 0.853209961006406 0.293580077987189 0.146790038993594 42 0.814077143304825 0.371845713390351 0.185922856695175 43 0.765352429596955 0.46929514080609 0.234647570403045 44 0.730075762299333 0.539848475401334 0.269924237700667 45 0.708690319932823 0.582619360134355 0.291309680067177 46 0.77107173531422 0.45785652937156 0.22892826468578 47 0.869828861883438 0.260342276233123 0.130171138116562 48 0.825759005436952 0.348481989126096 0.174240994563048 49 0.840527924461918 0.318944151076163 0.159472075538082 50 0.829955661480354 0.340088677039291 0.170044338519646 51 0.774194125611997 0.451611748776007 0.225805874388003 52 0.682160839622631 0.635678320754738 0.317839160377369 53 0.570498245788555 0.85900350842289 0.429501754211445 54 0.493600414601984 0.987200829203968 0.506399585398016 55 0.395015190843037 0.790030381686075 0.604984809156963 56 0.302407533746764 0.604815067493528 0.697592466253236 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 = 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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