H2: multiple lineair regression France (default values)

*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: Thu, 11 Dec 2008 14:28:59 -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/11/t1229031015o1t27s69uh21e7h.htm/, Retrieved Thu, 11 Dec 2008 21:30:25 +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/Dec/11/t1229031015o1t27s69uh21e7h.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:

Dataseries X:

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3258.1 0 3140.1 0 3627.4 0 3279.4 0 3204 0 3515.6 0 3146.6 0 2271.7 0 3627.9 0 3553.4 0 3018.3 0 3355.4 0 3242 0 3311.1 0 4125.2 1 3423 0 3120.3 0 3863 0 3240.8 0 2837.4 0 3945 0 3684.1 0 3659.6 0 3769.6 0 3592.7 0 3754 0 4507.8 1 3853.2 0 3817.2 0 3958.4 0 3428.9 0 3125.7 0 3977 0 3983.3 0 4299.6 0 4306.9 0 4259.5 0 3986 0 4755.6 1 3925.6 0 4206.5 0 4323.4 0 3816.1 0 3410.7 0 4227.4 0 4296.9 0 4351.7 0 3800 0 4277 0 4100.2 0 4672.5 0 4189.9 0 4231.9 0 4654.9 0 4298.5 0 3635.9 0 4505.1 0 4891.9 0 4894.2 0 4093.2 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation France[t] = + 3793.67894736842 + 669.187719298246Dummy[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) 3793.67894736842 69.568282 54.5317 0 0 Dummy 669.187719298246 311.118814 2.1509 0.035662 0.017831 Multiple Linear Regression - Regression Statistics Multiple R 0.271795934951372 R-squared 0.0738730302560904 Adjusted R-squared 0.0579053238811955 F-TEST (value) 4.62640209693712 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0356621237160227 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 525.229008532001 Sum Squared Residuals 16000199.6614035 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3258.1 3793.67894736842 -535.578947368424 2 3140.1 3793.67894736842 -653.57894736842 3 3627.4 3793.67894736842 -166.278947368421 4 3279.4 3793.67894736842 -514.278947368421 5 3204 3793.67894736842 -589.678947368421 6 3515.6 3793.67894736842 -278.078947368421 7 3146.6 3793.67894736842 -647.078947368421 8 2271.7 3793.67894736842 -1521.97894736842 9 3627.9 3793.67894736842 -165.778947368421 10 3553.4 3793.67894736842 -240.278947368421 11 3018.3 3793.67894736842 -775.37894736842 12 3355.4 3793.67894736842 -438.278947368421 13 3242 3793.67894736842 -551.678947368421 14 3311.1 3793.67894736842 -482.578947368421 15 4125.2 4462.86666666667 -337.666666666667 16 3423 3793.67894736842 -370.678947368421 17 3120.3 3793.67894736842 -673.378947368421 18 3863 3793.67894736842 69.321052631579 19 3240.8 3793.67894736842 -552.878947368421 20 2837.4 3793.67894736842 -956.278947368421 21 3945 3793.67894736842 151.321052631579 22 3684.1 3793.67894736842 -109.578947368421 23 3659.6 3793.67894736842 -134.078947368421 24 3769.6 3793.67894736842 -24.0789473684211 25 3592.7 3793.67894736842 -200.978947368421 26 3754 3793.67894736842 -39.678947368421 27 4507.8 4462.86666666667 44.933333333333 28 3853.2 3793.67894736842 59.5210526315788 29 3817.2 3793.67894736842 23.5210526315788 30 3958.4 3793.67894736842 164.721052631579 31 3428.9 3793.67894736842 -364.778947368421 32 3125.7 3793.67894736842 -667.978947368421 33 3977 3793.67894736842 183.321052631579 34 3983.3 3793.67894736842 189.621052631579 35 4299.6 3793.67894736842 505.921052631579 36 4306.9 3793.67894736842 513.221052631579 37 4259.5 3793.67894736842 465.821052631579 38 3986 3793.67894736842 192.321052631579 39 4755.6 4462.86666666667 292.733333333333 40 3925.6 3793.67894736842 131.921052631579 41 4206.5 3793.67894736842 412.821052631579 42 4323.4 3793.67894736842 529.721052631579 43 3816.1 3793.67894736842 22.4210526315789 44 3410.7 3793.67894736842 -382.978947368421 45 4227.4 3793.67894736842 433.721052631579 46 4296.9 3793.67894736842 503.221052631579 47 4351.7 3793.67894736842 558.021052631579 48 3800 3793.67894736842 6.32105263157901 49 4277 3793.67894736842 483.321052631579 50 4100.2 3793.67894736842 306.521052631579 51 4672.5 3793.67894736842 878.821052631579 52 4189.9 3793.67894736842 396.221052631579 53 4231.9 3793.67894736842 438.221052631579 54 4654.9 3793.67894736842 861.221052631579 55 4298.5 3793.67894736842 504.821052631579 56 3635.9 3793.67894736842 -157.778947368421 57 4505.1 3793.67894736842 711.42105263158 58 4891.9 3793.67894736842 1098.22105263158 59 4894.2 3793.67894736842 1100.52105263158 60 4093.2 3793.67894736842 299.521052631579 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0873162693119841 0.174632538623968 0.912683730688016 6 0.0444685070280007 0.0889370140560015 0.955531492972 7 0.0228749233692268 0.0457498467384537 0.977125076630773 8 0.462205515667099 0.924411031334198 0.537794484332901 9 0.431835869282516 0.863671738565033 0.568164130717484 10 0.368690252728132 0.737380505456264 0.631309747271868 11 0.337395242287608 0.674790484575216 0.662604757712392 12 0.269391727791805 0.538783455583609 0.730608272208195 13 0.217812383496721 0.435624766993443 0.782187616503279 14 0.173712410625505 0.347424821251011 0.826287589374495 15 0.125588720887531 0.251177441775062 0.874411279112469 16 0.0999905467076243 0.199981093415249 0.900009453292376 17 0.097066488906937 0.194132977813874 0.902933511093063 18 0.138533850057291 0.277067700114583 0.861466149942709 19 0.129865368706544 0.259730737413088 0.870134631293456 20 0.273507953764155 0.547015907528311 0.726492046235845 21 0.364842630607527 0.729685261215055 0.635157369392473 22 0.362229318415726 0.724458636831453 0.637770681584274 23 0.354615760404278 0.709231520808556 0.645384239595722 24 0.357731698496937 0.715463396993875 0.642268301503063 25 0.34873299513423 0.69746599026846 0.65126700486577 26 0.346043986213504 0.692087972427009 0.653956013786496 27 0.303140793960018 0.606281587920035 0.696859206039983 28 0.307872633656825 0.61574526731365 0.692127366343175 29 0.303272063182688 0.606544126365376 0.696727936817312 30 0.31245023961356 0.62490047922712 0.68754976038644 31 0.356029262230818 0.712058524461636 0.643970737769182 32 0.625687566796593 0.748624866406815 0.374312433203407 33 0.641360031311134 0.717279937377732 0.358639968688866 34 0.649501965096152 0.700996069807697 0.350498034903848 35 0.70927147788823 0.581457044223540 0.290728522111770 36 0.744494263620151 0.511011472759697 0.255505736379848 37 0.751603180978295 0.496793638043411 0.248396819021705 38 0.726129522005496 0.547740955989009 0.273870477994504 39 0.67115927711569 0.65768144576862 0.32884072288431 40 0.64398629959796 0.712027400804079 0.356013700402040 41 0.617685729529144 0.764628540941712 0.382314270470856 42 0.603039616433829 0.793920767132342 0.396960383566171 43 0.588169658010124 0.823660683979752 0.411830341989876 44 0.78639686888795 0.427206262224100 0.213603131112050 45 0.749277586284487 0.501444827431027 0.250722413715513 46 0.706890040939692 0.586219918120616 0.293109959060308 47 0.659963289719765 0.68007342056047 0.340036710280235 48 0.69611942558489 0.607761148830222 0.303880574415111 49 0.630410462966955 0.73917907406609 0.369589537033045 50 0.577103843471961 0.845792313056078 0.422896156528039 51 0.563118236156004 0.873763527687992 0.436881763843996 52 0.472603904342445 0.94520780868489 0.527396095657555 53 0.372971366535662 0.745942733071324 0.627028633464338 54 0.307192370832541 0.614384741665082 0.692807629167459 55 0.194764224694670 0.389528449389339 0.80523577530533 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 1 0.0196078431372549 OK 10% type I error level 2 0.0392156862745098 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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