MRLM 3

*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: Tue, 21 Dec 2010 16:43:33 +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/21/t1292949692pvy598yo1s9upli.htm/, Retrieved Tue, 21 Dec 2010 17:41:43 +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/21/t1292949692pvy598yo1s9upli.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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216.234 627 1,59 213.586 696 1,26 209.465 825 1,13 204.045 677 1,92 200.237 656 2,61 203.666 785 2,26 241.476 412 2,41 260.307 352 2,26 243.324 839 2,03 244.460 729 2,86 233.575 696 2,55 237.217 641 2,27 235.243 695 2,26 230.354 638 2,57 227.184 762 3,07 221.678 635 2,76 217.142 721 2,51 219.452 854 2,87 256.446 418 3,14 265.845 367 3,11 248.624 824 3,16 241.114 687 2,47 229.245 601 2,57 231.805 676 2,89 219.277 740 2,63 219.313 691 2,38 212.610 683 1,69 214.771 594 1,96 211.142 729 2,19 211.457 731 1,87 240.048 386 1,6 240.636 331 1,63 230.580 707 1,22 208.795 715 1,21 197.922 657 1,49 194.596 653 1,64 194.581 642 1,66 185.686 643 1,77 178.106 718 1,82 172.608 654 1,78 167.302 632 1,28 168.053 731 1,29 202.300 392 1,37 202.388 344 1,12 182.516 792 1,51 173.476 852 2,24 166.444 649 2,94 171.297 629 3,09 169.701 685 3,46 164.182 617 3,64 161.914 715 4,39 159.612 715 4,15 151.001 629 5,21 158.114 916 5,8 186.530 531 5,91 187.069 357 5,39 174.330 917 5,46 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation werklozen[t] = + 273.528545729345 -0.0807404010605316faillissementen[t] -5.13190252585901inflatie[t] -2.01386020000994M1[t] -6.77892713905306M2[t] -2.47415427551693M3[t] -13.9725213667513M4[t] -18.0507397840908M5[t] -3.49531102402766M6[t] -1.62498432311486M7[t] -3.3458629590783M8[t] + 20.7067417985075M9[t] + 7.14096833442247M10[t] -6.47605899476825M11[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) 273.528545729345 33.563051 8.1497 0 0 faillissementen -0.0807404010605316 0.043516 -1.8554 0.068622 0.034311 inflatie -5.13190252585901 2.020593 -2.5398 0.013793 0.006897 M1 -2.01386020000994 15.014297 -0.1341 0.893765 0.446882 M2 -6.77892713905306 15.050385 -0.4504 0.65409 0.327045 M3 -2.47415427551693 15.38373 -0.1608 0.872787 0.436393 M4 -13.9725213667513 15.054236 -0.9281 0.357179 0.178589 M5 -18.0507397840908 15.034348 -1.2006 0.234774 0.117387 M6 -3.49531102402766 15.805485 -0.2211 0.825756 0.412878 M7 -1.62498432311486 18.826504 -0.0863 0.931514 0.465757 M8 -3.3458629590783 21.385939 -0.1565 0.87622 0.43811 M9 20.7067417985075 16.154721 1.2818 0.205021 0.102511 M10 7.14096833442247 15.295383 0.4669 0.642341 0.321171 M11 -6.47605899476825 15.004842 -0.4316 0.667634 0.333817 Multiple Linear Regression - Regression Statistics Multiple R 0.546521199731197 R-squared 0.298685421755627 Adjusted R-squared 0.141494223183613 F-TEST (value) 1.9001408760096 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0.048996741863215 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25.9845199937707 Sum Squared Residuals 39161.3261997867 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 216.234 212.730729048265 3.50327095173479 2 213.586 204.08810226958 9.49789773042016 3 209.465 198.644510724669 10.8204892753310 4 204.045 195.041519994965 9.00348000503526 5 200.237 189.117837257054 11.1191627429463 6 203.666 195.053920164359 8.61207983564108 7 241.476 226.270631081971 15.2053689180289 8 260.307 230.163961888518 30.1430381114815 9 243.324 216.076328910573 27.2476710894271 10 244.46 207.132520466683 37.3274795333166 11 233.575 197.770816155507 35.8041838444935 12 237.217 210.124529915845 27.0924700841555 13 235.243 203.802007083824 31.4409929161755 14 230.354 202.048253222215 28.3057467777846 15 227.184 193.775265091316 33.4087349086839 16 221.678 194.121818717786 27.5561812822145 17 217.142 184.382901440705 32.7590985592950 18 219.452 186.352371950408 33.0996280495917 19 256.446 222.039899831731 34.4061001682691 20 265.845 224.590738725630 41.2542612743697 21 248.624 211.488385072260 37.1356149277397 22 241.114 212.525059296311 28.5889407036892 23 229.245 205.33851620574 23.9064837942601 24 231.805 204.116836312693 27.6881636873066 25 219.277 198.269885101533 21.0071148984672 26 219.313 198.744073445920 20.5689265540796 27 212.61 207.235782260784 5.3742177392165 28 214.771 201.537697181955 13.2333028180455 29 211.142 185.379187040496 25.7628129595043 30 211.457 201.415343806713 10.0416561932873 31 240.048 232.526722555491 7.52127744450922 32 240.636 235.092608902081 5.54339109791917 33 230.58 230.890902896509 -0.310902896508924 34 208.795 216.730525249198 -7.93552524919824 35 197.922 206.359508474278 -8.43750847427783 36 194.596 212.388743694409 -17.7927436944093 37 194.581 211.160389855548 -16.5793898555481 38 185.686 205.7500732376 -20.0640732375999 39 178.106 203.742720895303 -25.6367208953032 40 172.608 197.617015572977 -25.0090155729772 41 167.302 197.881037241899 -30.5790372418989 42 168.053 204.391847271711 -36.3388472717109 43 202.3 233.222617730075 -30.9226177300751 44 202.388 236.660253976482 -34.272253976482 45 182.516 222.539717073865 -40.0237170738647 46 173.476 200.383230702271 -26.9072307022706 47 166.444 199.564173020267 -33.1201730202665 48 171.297 206.885254657367 -35.5882546573666 49 169.701 198.451128063399 -28.750128063399 50 164.182 198.252665941817 -34.0706659418174 51 161.914 190.795952607027 -28.8819526070272 52 159.612 180.529242121999 -20.9172421219989 53 151.001 177.954881518455 -26.9538815184546 54 158.114 166.309992683888 -8.19599268388838 55 186.53 198.700864515261 -12.1708645152614 56 187.069 213.697404977277 -26.6284049772771 57 174.33 192.176151964155 -17.8461519641551 58 169.362 189.593882063593 -20.2318820635930 59 166.827 193.774108852523 -26.9471088525233 60 178.037 190.7563779764 -12.7193779763999 61 186.413 197.034860847430 -10.6218608474304 62 189.226 193.463831882867 -4.237831882867 63 191.563 186.647768420901 4.91523157909905 64 188.906 192.772706410319 -3.86670641031909 65 186.005 198.113155501392 -12.1081555013921 66 195.309 202.527524122921 -7.21852412292088 67 223.532 237.571264285471 -14.0392642854707 68 226.899 242.939031530011 -16.0400315300113 69 214.126 220.328514082638 -6.20251408263816 70 206.903 217.744782221944 -10.8417822219439 71 204.442 195.647877291686 8.7941227083141 72 220.375 209.055257443286 11.3197425567138 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0192552238408009 0.0385104476816019 0.9807447761592 18 0.00493835878009705 0.0098767175601941 0.995061641219903 19 0.00118683046483447 0.00237366092966894 0.998813169535166 20 0.00082008579166887 0.00164017158333774 0.999179914208331 21 0.000561935051970587 0.00112387010394117 0.99943806494803 22 0.000306269071259202 0.000612538142518404 0.99969373092874 23 0.000148844332089442 0.000297688664178883 0.99985115566791 24 0.000461472818503879 0.000922945637007757 0.999538527181496 25 0.00175580075708124 0.00351160151416248 0.998244199242919 26 0.00162976887361513 0.00325953774723026 0.998370231126385 27 0.000897329815156769 0.00179465963031354 0.999102670184843 28 0.000907182849512661 0.00181436569902532 0.999092817150487 29 0.00162134293536212 0.00324268587072424 0.998378657064638 30 0.00247559293669513 0.00495118587339025 0.997524407063305 31 0.0036047374183564 0.0072094748367128 0.996395262581644 32 0.0151908093620440 0.0303816187240879 0.984809190637956 33 0.0785048810334825 0.157009762066965 0.921495118966517 34 0.322446311993162 0.644892623986323 0.677553688006838 35 0.644400325846617 0.711199348306767 0.355599674153383 36 0.835210796369447 0.329578407261107 0.164789203630553 37 0.927163556711461 0.145672886577078 0.072836443288539 38 0.97279135967719 0.0544172806456219 0.0272086403228110 39 0.990719119129817 0.0185617617403662 0.00928088087018312 40 0.994572626075356 0.0108547478492869 0.00542737392464347 41 0.993268851369952 0.0134622972600958 0.0067311486300479 42 0.991530015447667 0.0169399691046665 0.00846998455233327 43 0.98876869855793 0.0224626028841405 0.0112313014420702 44 0.990056222597773 0.0198875548044548 0.00994377740222739 45 0.993394082179536 0.0132118356409273 0.00660591782046363 46 0.99776001559396 0.00447996881208183 0.00223998440604091 47 0.998773957347637 0.00245208530472594 0.00122604265236297 48 0.999115019611331 0.00176996077733785 0.000884980388668926 49 0.998991464190695 0.00201707161860933 0.00100853580930466 50 0.998620945986379 0.00275810802724261 0.00137905401362130 51 0.996854115869735 0.00629176826052887 0.00314588413026444 52 0.992600936006362 0.0147981279872765 0.00739906399363825 53 0.97992888798724 0.0401422240255182 0.0200711120127591 54 0.94950464905732 0.10099070188536 0.05049535094268 55 0.901681555310639 0.196636889378723 0.0983184446893614 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.512820512820513 NOK 5% type I error level 31 0.794871794871795 NOK 10% type I error level 32 0.82051282051282 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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