Model 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: Mon, 27 Dec 2010 20:35:26 +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/27/t1293481988e1c9aed1rdlhne7.htm/, Retrieved Mon, 27 Dec 2010 21:33:19 +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/27/t1293481988e1c9aed1rdlhne7.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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4.24 3.353 4.15 3.186 3.93 3.902 3.7 4.164 3.7 3.499 3.65 4.145 3.55 3.796 3.43 3.711 3.47 3.949 3.58 3.74 3.67 3.243 3.72 4.407 3.8 4.814 3.76 3.908 3.63 5.25 3.48 3.937 3.41 4.004 3.43 5.56 3.5 3.922 3.62 3.759 3.58 4.138 3.52 4.634 3.45 3.996 3.36 4.308 3.27 4.143 3.21 4.429 3.19 5.219 3.16 4.929 3.12 5.761 3.06 5.592 3.01 4.163 2.98 4.962 2.97 5.208 3.02 4.755 3.07 4.491 3.18 5.732 3.29 5.731 3.43 5.04 3.61 6.102 3.74 4.904 3.87 5.369 3.88 5.578 4.09 4.619 4.19 4.731 4.2 5.011 4.29 5.299 4.37 4.146 4.47 4.625 4.61 4.736 4.65 4.219 4.69 5.116 4.82 4.205 4.86 4.121 4.87 5.103 5.01 4.3 5.03 4.578 5.13 3.809 5.18 5.657 5.21 4.248 5.26 3.83 5.25 4.736 5.2 4.839 5.16 4.411 5.19 4.57 5.39 4.104 5.58 4.801 5.76 3.953 5.89 3.828 5.98 4.44 6.02 4.026 5.62 4.109 4.87 4.785

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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Lening[t] = + 5.81626032635842 -0.720281686285502Huis[t] + 0.344800910424701M1[t] + 0.0683670175317298M2[t] + 0.523080867088162M3[t] + 0.06870129434296M4[t] + 0.090616555068113M5[t] + 0.542015569238084M6[t] -0.145692405505592M7[t] -0.0503724973217004M8[t] + 0.0603553919736134M9[t] + 0.254510041466049M10[t] -0.287003756254083M11[t] + 0.0393050678176038t + 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) 5.81626032635842 0.414094 14.0457 0 0 Huis -0.720281686285502 0.086582 -8.3191 0 0 M1 0.344800910424701 0.233715 1.4753 0.145539 0.07277 M2 0.0683670175317298 0.234453 0.2916 0.771631 0.385816 M3 0.523080867088162 0.236629 2.2105 0.031025 0.015513 M4 0.06870129434296 0.233125 0.2947 0.769278 0.384639 M5 0.090616555068113 0.23291 0.3891 0.698654 0.349327 M6 0.542015569238084 0.23781 2.2792 0.026352 0.013176 M7 -0.145692405505592 0.235709 -0.6181 0.538928 0.269464 M8 -0.0503724973217004 0.234059 -0.2152 0.830356 0.415178 M9 0.0603553919736134 0.232779 0.2593 0.796336 0.398168 M10 0.254510041466049 0.232423 1.095 0.278031 0.139015 M11 -0.287003756254083 0.237392 -1.209 0.231574 0.115787 t 0.0393050678176038 0.002436 16.1371 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.908800495395926 R-squared 0.82591834043188 Adjusted R-squared 0.786900037425232 F-TEST (value) 21.167459289328 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.402271431608897 Sum Squared Residuals 9.38569367194293 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.24 3.78526181048541 0.454738189514593 2 4.15 3.66842002701975 0.481579972980247 3 3.93 3.64671725701337 0.283282742986631 4 3.7 3.04292895027897 0.657071049721031 5 3.7 3.58313660020158 0.116863399798416 6 3.65 3.60853871284873 0.0414612871512739 7 3.55 3.21151411443629 0.338485885563707 8 3.43 3.40736303377206 0.0226369662279445 9 3.47 3.38596894954902 0.0840310504509767 10 3.58 3.76996753929273 -0.189967539292733 11 3.67 3.6257388074741 0.0442611925259010 12 3.72 3.11363974870946 0.606360251290538 13 3.8 3.20459108063357 0.595408919366432 14 3.76 3.62003746333286 0.139962536667135 15 3.63 3.14743835771176 0.482561642288243 16 3.48 3.67809370687702 -0.198093706877023 17 3.41 3.69105516243865 -0.281055162438651 18 3.43 3.06100094056599 0.368999059434015 19 3.5 3.59241943577556 -0.0924194357755647 20 3.62 3.8444503266416 -0.224450326641597 21 3.58 3.72149652465231 -0.141496524652309 22 3.52 3.59769652556474 -0.0776965255647397 23 3.45 3.55502751151236 -0.105027511512361 24 3.36 3.65660844946297 -0.296608449462972 25 3.27 4.15956090594238 -0.889560905942384 26 3.21 3.71643151858936 -0.506431518589363 27 3.19 3.64142790379785 -0.451427903797852 28 3.16 3.43523508789305 -0.27523508789305 29 3.12 2.89718105344627 0.222818946553732 30 3.06 3.50961274041609 -0.449612740416095 31 3.01 3.89049236319200 -0.880492363192005 32 2.98 3.44961227185138 -0.469612271851384 33 2.97 3.42245593413807 -0.452455934138067 34 3.02 3.98220325533544 -0.96220325533544 35 3.07 3.67014889061228 -0.600148890612283 36 3.18 3.10258814200366 0.0774118579963379 37 3.29 3.48741440193225 -0.197414401932252 38 3.43 3.74800022208017 -0.318000222080167 39 3.61 3.477079988619 0.132920011381001 40 3.74 3.92490294386143 -0.184902943861433 41 3.87 3.65119228828143 0.218807711718569 42 3.88 3.99135749783534 -0.111357497835337 43 4.09 4.03370472805706 0.0562952719429393 44 4.19 4.08765815519458 0.102341844805421 45 4.2 4.03601224014756 0.163987759852444 46 4.29 4.06203083180737 0.227969168192629 47 4.37 4.39030688619203 -0.020306886192026 48 4.47 4.37160078253296 0.0983992174670415 49 4.61 4.67575549359757 -0.0657554935975716 50 4.65 4.81101230033181 -0.161012300331809 51 4.69 4.65893854510775 0.0310614548922505 52 4.82 4.90004065638624 -0.0800406563862439 53 4.86 5.02176464657698 -0.161764646576982 54 4.87 4.8051521126322 0.0648478873678043 55 5.01 4.73513539979338 0.274864600206619 56 5.03 4.66952206700751 0.360477932992494 57 5.13 5.37345164087398 -0.243451640873975 58 5.18 4.27583080192841 0.904169198071592 59 5.21 4.78849896800215 0.421501031997849 60 5.26 5.41588553694118 -0.155885536941177 61 5.25 5.14741630740882 0.102583692591183 62 5.2 4.83609846864604 0.363901531353957 63 5.16 5.63839794775027 -0.478397947750274 64 5.19 5.10879865470328 0.0812013452967193 65 5.39 5.50567024905508 -0.115670249055083 66 5.58 5.49433799570166 0.0856620042983383 67 5.76 5.45673395874570 0.303266041254305 68 5.89 5.68139414553288 0.208605854467122 69 5.98 5.39061471063907 0.589385289360931 70 6.02 5.92227104607131 0.0977289539286929 71 5.62 5.36027893620708 0.259721063792920 72 4.87 5.19967734034977 -0.329677340349768 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00473135448570717 0.00946270897141433 0.995268645514293 18 0.00423755700016801 0.00847511400033601 0.995762442999832 19 0.00465939269916059 0.00931878539832118 0.99534060730084 20 0.0177840230557236 0.0355680461114472 0.982215976944276 21 0.0154548861630617 0.0309097723261234 0.984545113836938 22 0.0111306906367309 0.0222613812734617 0.98886930936327 23 0.00653611118463468 0.0130722223692694 0.993463888815365 24 0.0151353194117487 0.0302706388234973 0.984864680588251 25 0.0788371699095617 0.157674339819123 0.921162830090438 26 0.102808095244982 0.205616190489964 0.897191904755018 27 0.0809845795338705 0.161969159067741 0.91901542046613 28 0.0546238430742144 0.109247686148429 0.945376156925786 29 0.036215655634078 0.072431311268156 0.963784344365922 30 0.0208898570995996 0.0417797141991992 0.9791101429004 31 0.0153044671067144 0.0306089342134288 0.984695532893286 32 0.0116454581785980 0.0232909163571960 0.988354541821402 33 0.0104331645350244 0.0208663290700488 0.989566835464976 34 0.0290155662860652 0.0580311325721304 0.970984433713935 35 0.0493302624156953 0.0986605248313906 0.950669737584305 36 0.0347924869189832 0.0695849738379663 0.965207513081017 37 0.0383376645716353 0.0766753291432707 0.961662335428365 38 0.0845925869623556 0.169185173924711 0.915407413037644 39 0.241990604832792 0.483981209665583 0.758009395167208 40 0.555124764012402 0.889750471975197 0.444875235987599 41 0.77717625062882 0.445647498742361 0.222823749371180 42 0.860230155180486 0.279539689639029 0.139769844819514 43 0.929781850529812 0.140436298940377 0.0702181494701884 44 0.95743436854226 0.0851312629154817 0.0425656314577408 45 0.967674848863916 0.0646503022721676 0.0323251511360838 46 0.98403446788769 0.0319310642246187 0.0159655321123093 47 0.984896862406333 0.0302062751873347 0.0151031375936674 48 0.979994407428888 0.0400111851422249 0.0200055925711125 49 0.96488158300279 0.0702368339944195 0.0351184169972097 50 0.945938959128318 0.108122081743364 0.0540610408716822 51 0.918859989107524 0.162280021784953 0.0811400108924765 52 0.855349070536841 0.289301858926317 0.144650929463159 53 0.754666077426988 0.490667845146025 0.245333922573012 54 0.630613434232626 0.738773131534749 0.369386565767374 55 0.497317882110341 0.994635764220681 0.502682117889659 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0769230769230769 NOK 5% type I error level 15 0.384615384615385 NOK 10% type I error level 23 0.58974358974359 NOK

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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