verbetering

*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: Fri, 27 Nov 2009 02:27:31 -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/27/t1259314098m7v5rtkitngm3hx.htm/, Retrieved Fri, 27 Nov 2009 10:28:30 +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/27/t1259314098m7v5rtkitngm3hx.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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No (this computation is public)

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Dataseries X:

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7,6 0 7,5 7,7 8,1 8 7,8 0 7,6 7,5 7,7 8,1 7,8 0 7,8 7,6 7,5 7,7 7,8 0 7,8 7,8 7,6 7,5 7,5 0 7,8 7,8 7,8 7,6 7,5 0 7,5 7,8 7,8 7,8 7,1 0 7,5 7,5 7,8 7,8 7,5 0 7,1 7,5 7,5 7,8 7,5 0 7,5 7,1 7,5 7,5 7,6 0 7,5 7,5 7,1 7,5 7,7 0 7,6 7,5 7,5 7,1 7,7 0 7,7 7,6 7,5 7,5 7,9 0 7,7 7,7 7,6 7,5 8,1 0 7,9 7,7 7,7 7,6 8,2 0 8,1 7,9 7,7 7,7 8,2 0 8,2 8,1 7,9 7,7 8,2 0 8,2 8,2 8,1 7,9 7,9 0 8,2 8,2 8,2 8,1 7,3 0 7,9 8,2 8,2 8,2 6,9 0 7,3 7,9 8,2 8,2 6,6 0 6,9 7,3 7,9 8,2 6,7 0 6,6 6,9 7,3 7,9 6,9 0 6,7 6,6 6,9 7,3 7 0 6,9 6,7 6,6 6,9 7,1 0 7 6,9 6,7 6,6 7,2 0 7,1 7 6,9 6,7 7,1 0 7,2 7,1 7 6,9 6,9 0 7,1 7,2 7,1 7 7 0 6,9 7,1 7,2 7,1 6,8 0 7 6,9 7,1 7,2 6,4 0 6,8 7 6,9 7,1 6,7 0 6,4 6,8 7 6,9 6,6 0 6,7 6,4 6,8 7 6,4 0 6,6 6,7 6,4 6,8 6,3 0 6,4 6,6 6,7 6,4 6,2 0 6,3 6,4 6,6 6,7 6,5 0 6,2 6,3 6,4 6,6 6,8 1 6,5 6,2 6,3 6,4 6,8 1 6,8 6,5 6,2 6,3 6,4 1 6,8 6,8 6,5 6,2 6,1 1 6,4 6,8 6,8 6,5 5,8 1 6,1 6,4 6,8 6,8 6,1 1 5,8 6,1 6,4 6,8 7,2 1 6,1 5,8 6,1 6,4 7,3 1 7,2 6,1 5,8 6,1 6,9 1 7,3 7 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] = -0.206618878764414 + 0.0835818229950486X[t] + 1.52890254510051`Y-1`[t] -0.711924325810514`Y-2`[t] -0.264801000441926`Y-3`[t] + 0.461488266484942`Y-4`[t] + 0.266355376773095M1[t] + 0.155434228591892M2[t] -0.0233346187909136M3[t] + 0.0582735063385753M4[t] + 0.113138663587701M5[t] -0.0762817036946616M6[t] -0.117538108379314M7[t] + 0.410083083239657M8[t] -0.348315498829714M9[t] -0.068081760433958M10[t] + 0.0996209060985931M11[t] + 0.00138288697974347t + 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) -0.206618878764414 0.544443 -0.3795 0.706371 0.353186 X 0.0835818229950486 0.105695 0.7908 0.433855 0.216927 `Y-1` 1.52890254510051 0.145638 10.498 0 0 `Y-2` -0.711924325810514 0.278027 -2.5606 0.014433 0.007217 `Y-3` -0.264801000441926 0.277183 -0.9553 0.345296 0.172648 `Y-4` 0.461488266484942 0.153193 3.0125 0.004534 0.002267 M1 0.266355376773095 0.138643 1.9212 0.062042 0.031021 M2 0.155434228591892 0.146075 1.0641 0.293841 0.14692 M3 -0.0233346187909136 0.148041 -0.1576 0.875568 0.437784 M4 0.0582735063385753 0.146148 0.3987 0.692267 0.346133 M5 0.113138663587701 0.145224 0.7791 0.440643 0.220322 M6 -0.0762817036946616 0.141797 -0.538 0.593658 0.296829 M7 -0.117538108379314 0.140423 -0.837 0.407677 0.203839 M8 0.410083083239657 0.139288 2.9441 0.005433 0.002717 M9 -0.348315498829714 0.159101 -2.1893 0.034626 0.017313 M10 -0.068081760433958 0.16833 -0.4045 0.688088 0.344044 M11 0.0996209060985931 0.157438 0.6328 0.530581 0.26529 t 0.00138288697974347 0.003385 0.4085 0.685157 0.342579 Multiple Linear Regression - Regression Statistics Multiple R 0.966437910189696 R-squared 0.934002234251826 Adjusted R-squared 0.905233977387238 F-TEST (value) 32.4664173657845 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.203197265081223 Sum Squared Residuals 1.61027601292307 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.6 7.5930891928012 0.00691080719879664 2 7.8 7.93089527809715 -0.130895278097154 3 7.8 7.85646228762755 -0.0564622876275469 4 7.8 7.6782906812335 0.121709318766505 5 7.5 7.72772735202247 -0.227727352022473 6 7.5 7.1733167614867 0.326683238513308 7 7.1 7.34702054152494 -0.247020541524937 8 7.5 7.34390390221603 0.156096097783973 9 7.5 7.34477247554533 0.155227524454675 10 7.6 7.44753977077339 0.152460229226610 11 7.7 7.47899987202499 0.221000127975014 12 7.7 7.64705498142911 0.0529450185708865 13 7.9 7.8171207125567 0.082879287443293 14 8.1 8.03303168697965 0.0669683130203491 15 8.2 8.06519019708308 0.134809802916919 16 8.2 8.10572639845187 0.0942736015481242 17 8.2 8.1301194633083 0.0698805366917033 18 7.9 8.00789953625847 -0.107899536258473 19 7.3 7.5555040816719 -0.255504081671909 20 6.9 7.38074393095347 -0.480743930953472 21 6.6 6.51876211344253 0.0812378865574694 22 6.7 6.64691182593176 0.0530881740682446 23 6.9 7.01149237198306 -0.111492371983060 24 7 7.04268742284186 -0.0426874228418621 25 7.1 7.15600449595297 -0.0560044959529722 26 7.2 7.12135268324062 0.0786473167593798 27 7.1 7.09148209801935 0.00851790198064515 28 6.9 6.97005914964179 -0.0700591496417848 29 7 6.81138784403591 0.188612155964093 30 6.8 6.99125441009813 -0.191254410098128 31 6.4 6.58121932423196 -0.181219324231957 32 6.7 6.52226949661139 0.177730503388607 33 6.6 6.607803322113 -0.00780332211300146 34 6.4 6.53657514211508 -0.136575142115077 35 6.3 6.20703701246177 0.0929629875382312 36 6.2 6.26322018398464 -0.0632201839846451 37 6.5 6.45607199924838 0.043928000751624 38 6.8 6.89416120390037 -0.0941612039003712 39 6.8 6.94219998268 -0.142199982680004 40 6.4 6.68602457026501 -0.286024570265010 41 6.1 6.18971777626658 -0.0897177762665835 42 5.8 5.9662257427035 -0.166225742703500 43 6.1 5.78717915938836 0.312820840611635 44 7.2 6.88327629279899 0.316723707201015 45 7.3 7.53546991976386 -0.235469919763855 46 6.9 6.96897326117978 -0.0689732611797782 47 6.1 6.30247074353018 -0.202470743530185 48 5.8 5.74703741174438 0.0529625882556206 49 6.2 6.27771359944074 -0.0777135994407418 50 7.1 7.0205591477822 0.0794408522177961 51 7.7 7.64466543459001 0.055334565409987 52 7.9 7.75989920040783 0.140100799592166 53 7.7 7.64104756436674 0.0589524356332608 54 7.4 7.26130354945321 0.138696450546792 55 7.5 7.12907689318283 0.370923106817168 56 8 8.16980637742012 -0.169806377420123 57 8.1 8.09319216913529 0.00680783086471272 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.86693160958983 0.266136780820341 0.133068390410171 22 0.811053117439573 0.377893765120854 0.188946882560427 23 0.781410494290239 0.437179011419522 0.218589505709761 24 0.72163067546098 0.55673864907804 0.27836932453902 25 0.700202775376297 0.599594449247406 0.299797224623703 26 0.599821421726036 0.800357156547929 0.400178578273964 27 0.489102143983505 0.97820428796701 0.510897856016495 28 0.395925698110509 0.791851396221017 0.604074301889491 29 0.63738544711802 0.72522910576396 0.36261455288198 30 0.618318511897711 0.763362976204577 0.381681488102289 31 0.640785667418245 0.71842866516351 0.359214332581755 32 0.639794659482982 0.720410681034037 0.360205340517018 33 0.518483824278609 0.963032351442783 0.481516175721391 34 0.446854921165211 0.893709842330422 0.553145078834789 35 0.68799860863488 0.624002782730239 0.312001391365119 36 0.866583284751526 0.266833430496947 0.133416715248474 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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