Multiple Regression werkloosh ecogr 4 vertragingen

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 17 Dec 2009 07:24:39 -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/17/t1261059973wnubrb2m4h16t1h.htm/, Retrieved Thu, 17 Dec 2009 15:26:25 +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/17/t1261059973wnubrb2m4h16t1h.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}, }

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Dataseries X:

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8,3 101,6 8,2 8,7 9,3 9,3 8,5 94,6 8,3 8,2 8,7 9,3 8,6 95,9 8,5 8,3 8,2 8,7 8,5 104,7 8,6 8,5 8,3 8,2 8,2 102,8 8,5 8,6 8,5 8,3 8,1 98,1 8,2 8,5 8,6 8,5 7,9 113,9 8,1 8,2 8,5 8,6 8,6 80,9 7,9 8,1 8,2 8,5 8,7 95,7 8,6 7,9 8,1 8,2 8,7 113,2 8,7 8,6 7,9 8,1 8,5 105,9 8,7 8,7 8,6 7,9 8,4 108,8 8,5 8,7 8,7 8,6 8,5 102,3 8,4 8,5 8,7 8,7 8,7 99 8,5 8,4 8,5 8,7 8,7 100,7 8,7 8,5 8,4 8,5 8,6 115,5 8,7 8,7 8,5 8,4 8,5 100,7 8,6 8,7 8,7 8,5 8,3 109,9 8,5 8,6 8,7 8,7 8 114,6 8,3 8,5 8,6 8,7 8,2 85,4 8 8,3 8,5 8,6 8,1 100,5 8,2 8 8,3 8,5 8,1 114,8 8,1 8,2 8 8,3 8 116,5 8,1 8,1 8,2 8 7,9 112,9 8 8,1 8,1 8,2 7,9 102 7,9 8 8,1 8,1 8 106 7,9 7,9 8 8,1 8 105,3 8 7,9 7,9 8 7,9 118,8 8 8 7,9 7,9 8 106,1 7,9 8 8 7,9 7,7 109,3 8 7,9 8 8 7,2 117,2 7,7 8 7,9 8 7,5 92,5 7,2 7,7 8 7,9 7,3 104,2 7,5 7,2 7,7 8 7 112,5 7,3 7,5 7,2 7,7 7 122,4 7 7,3 7,5 7,2 7 113,3 7 7 7,3 7,5 7,2 100 7 7 7 7,3 7,3 110,7 7,2 7 7 7 7,1 112,8 7,3 7,2 7 7 6,8 109,8 7,1 7,3 7,2 7 6,4 117,3 6,8 7,1 7,3 7,2 6,1 109,1 6,4 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.98590756285012 -0.00943061190311762X[t] + 1.52598349264715Y1[t] -0.930814478092821Y2[t] + 0.083898441498005Y3[t] + 0.200460686192801Y4[t] + 0.0943347310193463M1[t] + 0.0323584890565962M2[t] -0.132720980590720M3[t] + 0.0607190532369926M4[t] -0.026252010278004M5[t] -0.155003542088029M6[t] + 0.0471044771517931M7[t] + 0.38169268214532M8[t] -0.486310067426483M9[t] + 0.0920046044556282M10[t] + 0.123841822712825M11[t] -0.00251557949133382t + 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) 1.98590756285012 0.981443 2.0235 0.050101 0.02505 X -0.00943061190311762 0.004171 -2.2607 0.029585 0.014792 Y1 1.52598349264715 0.150629 10.1307 0 0 Y2 -0.930814478092821 0.289905 -3.2108 0.002693 0.001347 Y3 0.083898441498005 0.289711 0.2896 0.773702 0.386851 Y4 0.200460686192801 0.161051 1.2447 0.220862 0.110431 M1 0.0943347310193463 0.116215 0.8117 0.422005 0.211003 M2 0.0323584890565962 0.122634 0.2639 0.793312 0.396656 M3 -0.132720980590720 0.125244 -1.0597 0.29597 0.147985 M4 0.0607190532369926 0.119433 0.5084 0.614114 0.307057 M5 -0.026252010278004 0.115121 -0.228 0.82084 0.41042 M6 -0.155003542088029 0.110417 -1.4038 0.168498 0.084249 M7 0.0471044771517931 0.112013 0.4205 0.676469 0.338234 M8 0.38169268214532 0.142536 2.6779 0.010882 0.005441 M9 -0.486310067426483 0.15808 -3.0763 0.003874 0.001937 M10 0.0920046044556282 0.170344 0.5401 0.592272 0.296136 M11 0.123841822712825 0.141184 0.8772 0.385908 0.192954 t -0.00251557949133382 0.00295 -0.8528 0.399113 0.199557 Multiple Linear Regression - Regression Statistics Multiple R 0.97925484748044 R-squared 0.958940056313942 Adjusted R-squared 0.9405711341386 F-TEST (value) 52.2044814148763 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.162151251073433 Sum Squared Residuals 0.999135072537818 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.3 8.17909511284498 0.120904887155019 2 8.5 8.74828409812503 -0.248284098125033 3 8.6 8.6183188717678 -0.0183188717677956 4 8.5 8.60084889605629 -0.100848896056286 5 8.2 8.32042637551077 -0.120426375510767 6 8.1 7.91725152155756 0.182748478442443 7 7.9 8.1061425118694 -0.206142511869397 8 8.6 8.49209447838564 0.107905521614356 9 8.7 8.6678263836203 0.0321736163797068 10 8.7 8.54279222538737 0.157207774612629 11 8.5 8.56651265504675 -0.0665126550467537 12 8.4 8.25632210427889 0.143677895721114 13 8.5 8.46305084815029 0.0369491518497075 14 8.7 8.65858015475089 0.0414198452491076 15 8.7 8.63858633470873 0.0614136652912708 16 8.6 8.49211861279092 0.107881387209076 17 8.5 8.4264324336049 0.0735675663950994 18 8.3 8.18897892857799 0.111021071422013 19 8 8.12374239751187 -0.123742397511875 20 8.2 8.43112082564044 -0.23112082564044 21 8.1 7.96581554187862 0.134184458121378 22 8.1 8.00273396948358 0.0972660305164226 23 8 8.06574649826518 -0.0657464982651822 24 7.9 7.85244324273629 0.0475567572637083 25 7.9 7.96749309393357 -0.0674930939335735 26 8 7.9499704285265 0.0500295714734993 27 8 7.91313924421567 0.0868607557843335 28 7.9 7.8636229214314 0.0363770785686043 29 8 7.74969654447975 0.250303455520255 30 7.7 7.85397734078169 -0.153977340781686 31 7.2 7.41980160674232 -0.219801606742319 32 7.5 7.48940671888631 0.0105932811136916 33 7.3 7.42662905356713 -0.126629053567130 34 7 7.23762559859791 -0.237625598597911 35 7 6.82689121670033 0.17310878329967 36 7 7.10895524380063 -0.108955243800627 37 7.2 7.26093986395214 -0.060939863952142 38 7.3 7.34059898780629 -0.0405989878062894 39 7.1 7.11963510731724 -0.0196351073172426 40 6.8 6.95735293932386 -0.157352939323864 41 6.4 6.57398653625693 -0.173986536256931 42 6.1 6.1921677692498 -0.0921677692498036 43 6.5 6.17690112181211 0.323098878187889 44 7.7 7.49258308221601 0.207416917783991 45 7.9 7.93972902093396 -0.0397290209339552 46 7.5 7.51684820653114 -0.0168482065311401 47 6.9 6.94084962998773 -0.040849629987734 48 6.6 6.6822794091842 -0.0822794091841953 49 6.9 6.92942108111901 -0.0294210811190112 50 7.7 7.50256633079128 0.197433669208716 51 8 8.11032044199057 -0.110320441990566 52 8 7.88605663039753 0.113943369602470 53 7.7 7.72945811014766 -0.0294581101476566 54 7.3 7.34762443983297 -0.047624439832967 55 7.4 7.1734123620643 0.226587637935702 56 8.1 8.1947948948716 -0.0947948948715987 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.717185090280473 0.565629819439055 0.282814909719527 22 0.596302108247273 0.807395783505454 0.403697891752727 23 0.46859836062465 0.9371967212493 0.53140163937535 24 0.361765802520182 0.723531605040364 0.638234197479818 25 0.265362920123955 0.53072584024791 0.734637079876045 26 0.175802263187923 0.351604526375846 0.824197736812077 27 0.124093663653155 0.248187327306309 0.875906336346845 28 0.083972158475669 0.167944316951338 0.916027841524331 29 0.317015107409730 0.634030214819461 0.68298489259027 30 0.310402201215798 0.620804402431595 0.689597798784202 31 0.477852042778613 0.955704085557225 0.522147957221387 32 0.34415894208035 0.6883178841607 0.65584105791965 33 0.375432917915296 0.750865835830593 0.624567082084704 34 0.312644371539369 0.625288743078738 0.687355628460631 35 0.418579163694250 0.837158327388501 0.58142083630575 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 = 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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