mini-tutorial 2 link 1

*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: Wed, 01 Dec 2010 11:22:00 +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/01/t1291202560wwmhxjwnqpplhdm.htm/, Retrieved Wed, 01 Dec 2010 12:22:40 +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/01/t1291202560wwmhxjwnqpplhdm.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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-5 -6 33 5 15 -1 -3 24 6 17 -2 -4 24 6 13 -5 -7 31 5 12 -4 -7 25 5 13 -6 -7 28 3 10 -2 -3 24 5 14 -2 0 25 5 13 -2 -5 16 5 10 -2 -3 17 3 11 2 3 11 6 12 1 2 12 6 7 -8 -7 39 4 11 -1 -1 19 6 9 1 0 14 5 13 -1 -3 15 4 12 2 4 7 5 5 2 2 12 5 13 1 3 12 4 11 -1 0 14 3 8 -2 -10 9 2 8 -2 -10 8 3 8 -1 -9 4 2 8 -8 -22 7 -1 0 -4 -16 3 0 3 -6 -18 5 -2 0 -3 -14 0 1 -1 -3 -12 -2 -2 -1 -7 -17 6 -2 -4 -9 -23 11 -2 1 -11 -28 9 -6 -1 -13 -31 17 -4 0 -11 -21 21 -2 -1 -9 -19 21 0 6 -17 -22 41 -5 0 -22 -22 57 -4 -3 -25 -25 65 -5 -3 -20 -16 68 -1 4 -24 -22 73 -2 1 -24 -21 71 -4 0 -22 -10 71 -1 -4 -19 -7 70 1 -2 -18 -5 69 1 3 -17 -4 65 -2 2 -11 7 57 1 5 -11 6 57 1 6 -12 3 57 3 6 -10 10 55 3 3 -15 0 65 1 4 -15 -2 65 1 7 -15 -1 64 0 5 -13 2 60 2 6 -8 8 43 2 1 -13 -6 47 -1 3 -9 -4 40 1 6 -7 4 31 0 0 -4 7 27 1 3 -4 3 24 1 4 -2 3 23 3 7 0 8 17 2 6

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 werkloosheid[t] = + 0.663907484037988 -3.94105757478893indicator[t] + 1.00077195481772vooruitzichten[t] + 1.03740674497135financiën[t] + 0.888119561734235spaarvermogen[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) 0.663907484037988 0.4621 1.4367 0.156462 0.078231 indicator -3.94105757478893 0.030998 -127.1389 0 0 vooruitzichten 1.00077195481772 0.022989 43.5326 0 0 financiën 1.03740674497135 0.133596 7.7652 0 0 spaarvermogen 0.888119561734235 0.059123 15.0216 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.998682888644061 R-squared 0.997367512070446 Adjusted R-squared 0.997176058402843 F-TEST (value) 5209.44583905243 F-TEST (DF numerator) 4 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.22777002196627 Sum Squared Residuals 82.9080574761475 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 33 32.8733907799466 0.126609220053420 2 24 22.9251222136838 1.07487778631619 3 24 22.3129295867181 1.6870704132819 4 31 29.2082601399261 1.79173986007385 5 25 26.1553221268715 -1.15532212687145 6 28 29.2982651013039 -1.29826510130391 7 24 23.1644143582987 0.835585641701287 8 25 25.2786106610176 -0.278610661017639 9 16 17.6103922017263 -1.61039220172634 10 17 18.4252421831533 -1.42524218315331 11 11 12.6659834095522 -1.6659834095522 12 12 11.1656712208522 0.834328779147763 13 39 39.1059065575873 -0.105906557587348 14 19 17.8217096294454 1.1782903705546 15 14 13.4554379366509 0.544562063349145 16 15 16.4097109150700 -1.40971091506996 17 7 6.41251168725893 0.587488312741069 18 12 11.5159242714974 0.484075728502633 19 12 13.6441079326642 -1.64410793266420 20 14 14.8221417876148 -0.822141787614838 21 9 7.71807306925522 1.28192693074478 22 8 8.75547981422656 -0.755479814226566 23 4 4.77778744928401 -0.777787449284008 24 7 9.13797833138822 -2.13797833138822 25 3 3.08014519131288 -0.0801451913128814 26 5 4.2215442561099 0.778455743890102 27 0 -1.3744399758062 1.3744399758062 28 -2 -2.4851163010848 0.485116301084801 29 6 5.61089553877961 0.389104461220394 30 11 11.9289767681223 -0.928976768122314 31 9 8.8813660402577 0.118633959742295 32 17 16.7240983770593 0.275901622940668 33 21 20.0363967038671 0.96360329613286 34 21 22.4474758860071 -1.44747588600707 35 41 40.4578695246032 0.54213047539682 36 57 58.5362054583165 -1.53620545831647 37 65 66.3196555732587 -1.31965557325873 38 68 65.9877792046986 2.01222079530138 39 73 72.045612344774 0.95438765522605 40 71 70.0834512479147 0.916548752085263 41 71 72.7695695893089 -1.76956958930892 42 70 67.7997653428065 2.20023465719354 43 69 70.3008494863241 -1.30084948632414 44 65 63.3602240697047 1.63977593029534 45 57 56.4989490440828 0.501050955917244 46 57 56.3862966509993 0.613703349000729 47 57 59.3998518512777 -2.39985185127773 48 55 55.8587817002212 -0.85878170022122 49 65 64.3696560977802 0.630343902219807 50 65 65.0324708733475 -0.0324708733474578 51 64 63.2195969597254 0.78040304027464 52 60 61.3027307262776 -1.30273072627759 53 43 43.1614767725681 -0.161476772568106 54 47 47.5199761676191 -0.519976167619083 55 40 38.4964619532442 1.50353804675578 56 31 32.2543983268314 -1.25439832683137 57 27 27.1353068970918 -0.135306897091793 58 24 24.0203386395551 -0.0203386395551479 59 23 20.8773956651227 2.12260433487731 60 17 16.0736139829279 0.926386017072149 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.619893251925594 0.760213496148811 0.380106748074406 9 0.632630497329048 0.734739005341905 0.367369502670952 10 0.568921314545944 0.862157370908113 0.431078685454057 11 0.56325797692002 0.87348404615996 0.43674202307998 12 0.599634321552322 0.800731356895355 0.400365678447678 13 0.508522990301335 0.98295401939733 0.491477009698665 14 0.446447530437689 0.892895060875379 0.55355246956231 15 0.437711670656578 0.875423341313156 0.562288329343422 16 0.362327811537557 0.724655623075114 0.637672188462443 17 0.341197792631689 0.682395585263378 0.658802207368311 18 0.298890279478185 0.597780558956369 0.701109720521815 19 0.273606435143318 0.547212870286635 0.726393564856682 20 0.236480779403556 0.472961558807113 0.763519220596444 21 0.351342923983886 0.702685847967772 0.648657076016114 22 0.333620959124991 0.667241918249982 0.666379040875009 23 0.276673327562583 0.553346655125165 0.723326672437417 24 0.317458303043468 0.634916606086935 0.682541696956532 25 0.293698581199693 0.587397162399387 0.706301418800307 26 0.390913633381787 0.781827266763575 0.609086366618213 27 0.388050019929043 0.776100039858087 0.611949980070957 28 0.374680977273399 0.749361954546797 0.625319022726601 29 0.322680650148821 0.645361300297642 0.677319349851179 30 0.282232198721397 0.564464397442795 0.717767801278603 31 0.251203075053308 0.502406150106617 0.748796924946691 32 0.195061284684385 0.39012256936877 0.804938715315615 33 0.177456218735911 0.354912437471822 0.822543781264089 34 0.262573396750346 0.525146793500691 0.737426603249654 35 0.221188273501913 0.442376547003827 0.778811726498087 36 0.253978494014267 0.507956988028534 0.746021505985733 37 0.309718628775824 0.619437257551647 0.690281371224176 38 0.391557438172936 0.783114876345872 0.608442561827064 39 0.323476070957217 0.646952141914434 0.676523929042783 40 0.263809043613109 0.527618087226218 0.736190956386891 41 0.349815264061387 0.699630528122773 0.650184735938613 42 0.736438105146765 0.527123789706469 0.263561894853235 43 0.675469891859469 0.649060216281063 0.324530108140531 44 0.746812119984141 0.506375760031718 0.253187880015859 45 0.671243473660297 0.657513052679407 0.328756526339703 46 0.589219697809926 0.821560604380147 0.410780302190073 47 0.883858513758237 0.232282972483525 0.116141486241763 48 0.819557965626437 0.360884068747126 0.180442034373563 49 0.802688452074975 0.394623095850051 0.197311547925025 50 0.693692013174342 0.612615973651316 0.306307986825658 51 0.920603295077999 0.158793409844003 0.0793967049220015 52 0.992991222747437 0.0140175545051266 0.00700877725256332 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 0.0222222222222222 OK 10% type I error level 1 0.0222222222222222 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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