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: Fri, 20 Nov 2009 11:11:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740748h7f4hqex39h4lpm.htm/, Retrieved Fri, 20 Nov 2009 19:12:40 +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/2009/Nov/20/t1258740748h7f4hqex39h4lpm.htm/}, year = {2009}, } @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 = {2009}, 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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12,6 18 15,7 16 13,2 19 20,3 18 12,8 23 8 20 0,9 20 3,6 15 14,1 17 21,7 16 24,5 15 18,9 10 13,9 13 11 10 5,8 19 15,5 21 22,4 17 31,7 16 30,3 17 31,4 14 20,2 18 19,7 17 10,8 14 13,2 15 15,1 16 15,6 11 15,5 15 12,7 13 10,9 17 10 16 9,1 9 10,3 17 16,9 15 22 12 27,6 12 28,9 12 31 12 32,9 4 38,1 7 28,8 4 29 3 21,8 3 28,8 0 25,6 5 28,2 3 20,2 4 17,9 3 16,3 10 13,2 4 8,1 1 4,5 1 -0,1 8 0 5 2,3 4 2,8 0 2,9 2 0,1 7 3,5 6 8,6 9 13,8 10

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Rvnp[t] = + 38.2335095393206 -0.764949810543109Svdg[t] -3.59272407985997M1[t] -6.99181657027631M2[t] -5.0113105763478M3[t] -4.21864397615723M4[t] -4.17195730018391M5[t] -5.03620035897094M6[t] -7.09137315251833M7[t] -5.32674670389328M8[t] -2.80212025526823M9[t] -1.73337335194664M10[t] -1.26565656229918M11[t] -0.313696713864699t + 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) 38.2335095393206 10.70384 3.5719 0.000844 0.000422 Svdg -0.764949810543109 0.414666 -1.8447 0.07152 0.03576 M1 -3.59272407985997 6.680476 -0.5378 0.593311 0.296656 M2 -6.99181657027631 7.066713 -0.9894 0.327643 0.163821 M3 -5.0113105763478 6.651337 -0.7534 0.455031 0.227516 M4 -4.21864397615723 6.609334 -0.6383 0.526453 0.263226 M5 -4.17195730018391 6.592397 -0.6328 0.529969 0.264985 M6 -5.03620035897094 6.608617 -0.7621 0.449911 0.224955 M7 -7.09137315251833 6.754597 -1.0499 0.299268 0.149634 M8 -5.32674670389328 6.625689 -0.804 0.425559 0.21278 M9 -2.80212025526823 6.571308 -0.4264 0.671793 0.335896 M10 -1.73337335194664 6.580854 -0.2634 0.793421 0.396711 M11 -1.26565656229918 6.582159 -0.1923 0.848365 0.424182 t -0.313696713864699 0.147594 -2.1254 0.038955 0.019478 Multiple Linear Regression - Regression Statistics Multiple R 0.324935060040943 R-squared 0.105582793243811 Adjusted R-squared -0.147187286926416 F-TEST (value) 0.417702890993692 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.955563158999425 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.3815051824122 Sum Squared Residuals 4957.67989321279 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12.6 20.5579921558200 -7.95799215582005 2 15.7 18.3751025726251 -2.67510257262514 3 13.2 17.7470624210596 -4.54706242105963 4 20.3 18.9909821179286 1.30901788207140 5 12.8 14.8992230273217 -2.09922302732167 6 8 16.0161326862993 -8.01613268629927 7 0.9 13.6472631788872 -12.7472631788872 8 3.6 18.9229419663631 -15.3229419663631 9 14.1 19.6039720800372 -5.50397208003723 10 21.7 21.1239720800372 0.576027919962784 11 24.5 22.0429419663631 2.45705803363691 12 18.9 26.8196508675131 -7.91965086751312 13 13.9 20.6183806421591 -6.71838064215912 14 11 19.2004408695074 -8.2004408695074 15 5.8 13.9827018546832 -8.18270185468324 16 15.5 12.9317721199229 2.56822788007711 17 22.4 15.7245613242039 6.67543867579605 18 31.7 15.3115713620953 16.3884286379047 19 30.3 12.1777520441401 18.1222479558599 20 31.4 15.9235312105298 15.4764687894702 21 20.2 15.0746617031177 5.12533829688227 22 19.7 16.5946617031177 3.10533829688227 23 10.8 19.0435312105298 -8.24353121052981 24 13.2 19.2305412484212 -6.03054124842119 25 15.1 14.5591706441534 0.540829355846585 26 15.6 14.6711304925879 0.928869507412083 27 15.5 13.2781405304793 2.2218594695207 28 12.7 15.2870100378914 -2.58701003789138 29 10.9 11.9602007578276 -1.06020075782757 30 10 11.5472107957189 -1.54721079571894 31 9.1 14.5329899621086 -5.43298996210862 32 10.3 9.8643212125241 0.435678787475895 33 16.9 13.6051505683707 3.29484943162933 34 22 16.6550501894569 5.34494981054311 35 27.6 16.8090702652396 10.7909297347604 36 28.9 17.7610301136741 11.1389698863259 37 31 13.8546093199495 17.1453906800505 38 32.9 16.2614186000133 16.6385813999867 39 38.1 15.6333784484478 22.4666215515522 40 28.8 18.4071977664030 10.3928022335970 41 29 18.9051375390547 10.0948624609453 42 21.8 17.7271977664030 4.07280223359703 43 28.8 17.6531776906202 11.1468223093798 44 25.6 15.2793583726650 10.3206416273350 45 28.2 19.0201877285116 9.17981227148841 46 20.2 19.0102881074254 1.18971189257462 47 17.9 19.9292579937512 -2.02925799375125 48 16.3 15.5265691683840 0.773430831616032 49 13.2 16.2098472379180 -3.00984723791795 50 8.1 14.7919074652662 -6.69190746526624 51 4.5 16.4587167453301 -11.9587167453301 52 -0.1 11.5830379578542 -11.6830379578542 53 0 13.6108773515921 -13.6108773515921 54 2.3 13.1978873894835 -10.8978873894835 55 2.8 13.8888171242438 -11.0888171242438 56 2.9 13.8098472379180 -10.9098472379180 57 0.1 12.1960279199628 -12.0960279199628 58 3.5 13.7160279199628 -10.2160279199628 59 8.6 11.5751985641162 -2.97519856411621 60 13.8 11.7622086020076 2.03779139799241 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.111780849272206 0.223561698544412 0.888219150727794 18 0.443199970935922 0.886399941871844 0.556800029064078 19 0.710760990084942 0.578478019830116 0.289239009915058 20 0.7805086115887 0.4389827768226 0.2194913884113 21 0.676590160506361 0.646819678987278 0.323409839493639 22 0.5840496286447 0.8319007427106 0.4159503713553 23 0.694053223113498 0.611893553773005 0.305946776886502 24 0.757001413451101 0.485997173097798 0.242998586548899 25 0.717404683816405 0.56519063236719 0.282595316183595 26 0.670868609281358 0.658262781437284 0.329131390718642 27 0.599706365898895 0.80058726820221 0.400293634101105 28 0.653966143881173 0.692067712237654 0.346033856118827 29 0.611044312373871 0.777911375252257 0.388955687626129 30 0.574677226369177 0.850645547261646 0.425322773630823 31 0.651886823626854 0.696226352746292 0.348113176373146 32 0.631591957570217 0.736816084859567 0.368408042429783 33 0.635649885764143 0.728700228471715 0.364350114235857 34 0.634134665376294 0.731730669247412 0.365865334623706 35 0.670784666501184 0.658430666997632 0.329215333498816 36 0.820700085647692 0.358599828704615 0.179299914352308 37 0.81780175201184 0.364396495976319 0.182198247988160 38 0.754323776264018 0.491352447471964 0.245676223735982 39 0.74668728423805 0.506625431523899 0.253312715761950 40 0.700482288713771 0.599035422572457 0.299517711286229 41 0.670380602507146 0.659238794985708 0.329619397492854 42 0.533269911709523 0.933460176580955 0.466730088290477 43 0.434755036258003 0.869510072516006 0.565244963741997 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 0 0 OK

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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