*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: Mon, 06 Dec 2010 14:58:19 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/06/t1291647408hr3cqxo28ii6fx2.htm/, Retrieved Mon, 06 Dec 2010 15:56:48 +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/2010/Dec/06/t1291647408hr3cqxo28ii6fx2.htm/}, year = {2010}, } @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 = {2010}, 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:

Dataseries X:

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1635.25 8169.75 7977.64 10171 -14.9 -18 1.8 2.05 1833.42 7905.84 8334.59 9721 -16.2 -11 1.5 2.05 1910.43 8145.82 8623.36 9897 -14.4 -9 1 1.81 1959.67 8895.71 9098.03 9828 -17.3 -10 1.6 1.58 1969.6 9676.31 9154.34 9924 -15.7 -13 1.5 1.57 2061.41 9884.59 9284.73 10371 -12.6 -11 1.8 1.76 2093.48 10637.44 9492.49 10846 -9.4 -5 1.8 1.76 2120.88 10717.13 9682.35 10413 -8.1 -15 1.6 1.89 2174.56 10205.29 9762.12 10709 -5.4 -6 1.9 1.9 2196.72 10295.98 10124.63 10662 -4.6 -6 1.7 1.9 2350.44 10892.76 10540.05 10570 -4.9 -3 1.6 1.92 2440.25 10631.92 10601.61 10297 -4 -1 1.3 1.76 2408.64 11441.08 10323.73 10635 -3.1 -3 1.1 1.64 2472.81 11950.95 10418.4 10872 -1.3 -4 1.9 1.57 2407.6 11037.54 10092.96 10296 0 -6 2.6 1.69 2454.62 11527.72 10364.91 10383 -0.4 0 2.3 1.76 2448.05 11383.89 10152.09 10431 3 -4 2.4 1.89 2497.84 10989.34 10032.8 10574 0.4 -2 2.2 1.78 2645.64 11079.42 10204.59 10653 1.2 -2 2 1.88 2756.76 11028.93 10001.6 10805 0.6 -6 2.9 1.86 2849.27 10973 10411.75 10872 -1.3 -7 2.6 1.88 2921.44 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = + 131.464612932303 + 0.070054324911192Nikkei[t] + 0.106968905140376DJ_Indust[t] -0.0267508881683204Goudprijs[t] -17.0480085003543Conjunct_Seizoenzuiver[t] + 4.47598215700542Cons_vertrouw[t] + 0.150200966608876Alg_consumptie_index_BE[t] + 58.6738632349272Gem_rente_kasbon_1j[t] + 43.1906593467027t + 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) 131.464612932303 438.79514 0.2996 0.765957 0.382979 Nikkei 0.070054324911192 0.024175 2.8978 0.005949 0.002974 DJ_Indust 0.106968905140376 0.039394 2.7154 0.009568 0.004784 Goudprijs -0.0267508881683204 0.028804 -0.9287 0.35834 0.17917 Conjunct_Seizoenzuiver -17.0480085003543 3.711154 -4.5937 3.9e-05 2e-05 Cons_vertrouw 4.47598215700542 4.042054 1.1074 0.274443 0.137222 Alg_consumptie_index_BE 0.150200966608876 32.400339 0.0046 0.996323 0.498162 Gem_rente_kasbon_1j 58.6738632349272 58.128212 1.0094 0.318569 0.159285 t 43.1906593467027 3.562909 12.1223 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.996362636253447 R-squared 0.992738502921919 Adjusted R-squared 0.991355360621332 F-TEST (value) 717.74140845862 F-TEST (DF numerator) 8 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 77.9600135000791 Sum Squared Residuals 255266.075607166 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1635.25 1622.25715526697 12.992844733028 2 1833.42 1750.62945395148 82.7905460485205 3 1910.43 1800.92172596382 109.508274036181 4 1959.67 1980.82453903473 -21.1545390347251 5 1969.6 2040.84841939081 -71.2484193908069 6 2061.41 2067.91625432756 -6.50625432755852 7 2093.48 2145.66676577656 -52.1867657765631 8 2120.88 2167.00763458898 -46.1276345889771 9 2174.56 2169.84235032278 4.71764967721542 10 2196.72 2245.75237894843 -49.0323789484268 11 2350.44 2397.34896878969 -46.908968789691 12 2440.25 2420.33053455307 19.9194654469274 13 2408.64 2450.07395613777 -41.4339561377728 14 2472.81 2493.62059276989 -20.8105927698915 15 2407.6 2429.45111119588 -21.8511111958771 16 2454.62 2571.48107248847 -116.861072488466 17 2448.05 2512.32211804711 -64.2721180471125 18 2497.84 2558.07976706361 -60.2397670636074 19 2645.64 2616.04272737697 29.5972726230341 20 2756.76 2621.20317088031 135.556829119687 21 2849.27 2731.60032973916 117.669670260836 22 2921.44 2852.27879608347 69.1612039165264 23 2981.85 2885.42032402461 96.4296759753884 24 3080.58 3003.31282774214 77.2671722578587 25 3106.22 3073.39076198894 32.8292380110606 26 3119.31 3074.49275537600 44.8172446239966 27 3061.26 3093.79905614672 -32.5390561467211 28 3097.31 3141.15591343433 -43.8459134343331 29 3161.69 3220.67912274439 -58.9891227443882 30 3257.16 3289.27980872461 -32.1198087246116 31 3277.01 3288.56416487016 -11.5541648701549 32 3295.32 3317.20504089242 -21.8850408924247 33 3363.99 3446.9833116505 -82.9933116505012 34 3494.17 3588.8396434921 -94.6696434921018 35 3667.03 3662.85155632998 4.17844367001622 36 3813.06 3679.83356561616 133.226434383839 37 3917.96 3735.12558755312 182.834412446877 38 3895.51 3809.3093084191 86.2006915808982 39 3801.06 3780.37407956417 20.6859204358347 40 3570.12 3744.55683472340 -174.436834723404 41 3701.61 3753.65929445522 -52.0492944552206 42 3862.27 3893.07540824314 -30.8054082431406 43 3970.1 4016.00908258280 -45.9090825828049 44 4138.52 4145.6712627359 -7.15126273589644 45 4199.75 4180.76517212241 18.9848278775903 46 4290.89 4241.97079319684 48.9192068031583 47 4443.91 4387.76973385607 56.1402661439248 48 4502.64 4492.52633602426 10.1136639757393 49 4356.98 4477.92904891401 -120.949048914012 50 4591.27 4568.70486238589 22.5651376141057 51 4696.96 4685.53551949305 11.4244805069465 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.103235538167688 0.206471076335376 0.896764461832312 13 0.0722087093867136 0.144417418773427 0.927791290613286 14 0.0449325526985004 0.0898651053970007 0.9550674473015 15 0.0265261115489944 0.0530522230979889 0.973473888451006 16 0.0588092057765198 0.117618411553040 0.94119079422348 17 0.0451940462035627 0.0903880924071254 0.954805953796437 18 0.0629977844758274 0.125995568951655 0.937002215524173 19 0.148545188897247 0.297090377794494 0.851454811102753 20 0.45877606274951 0.91755212549902 0.54122393725049 21 0.369427366161381 0.738854732322763 0.630572633838619 22 0.346981392026407 0.693962784052815 0.653018607973593 23 0.302151898195495 0.604303796390989 0.697848101804505 24 0.231084001924839 0.462168003849678 0.768915998075161 25 0.163855426402507 0.327710852805014 0.836144573597493 26 0.395865531788272 0.791731063576544 0.604134468211728 27 0.71522965681489 0.569540686370219 0.284770343185109 28 0.738871317264728 0.522257365470545 0.261128682735272 29 0.67445074632177 0.651098507356459 0.325549253678229 30 0.657917582217589 0.684164835564822 0.342082417782411 31 0.846897286678738 0.306205426642524 0.153102713321262 32 0.862136545582364 0.275726908835273 0.137863454417637 33 0.788767572259573 0.422464855480853 0.211232427740427 34 0.729104562831827 0.541790874336345 0.270895437168173 35 0.771055908438449 0.457888183123102 0.228944091561551 36 0.830545514295195 0.338908971409611 0.169454485704805 37 0.872134530000992 0.255730939998017 0.127865469999008 38 0.836130497914184 0.327739004171633 0.163869502085816 39 0.738359284377287 0.523281431245427 0.261640715622713 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 3 0.107142857142857 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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