W7: Model 4

*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: Sun, 22 Nov 2009 06:34:45 -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/22/t1258896962m2idvh34mqhgeru.htm/, Retrieved Sun, 22 Nov 2009 14:36:14 +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/22/t1258896962m2idvh34mqhgeru.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:

cvm

Dataseries X:

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6,5 1,9 6,3 6,1 6,2 6,3 6,6 2 6,5 6,3 6,1 6,2 6,5 2,3 6,6 6,5 6,3 6,1 6,2 2,8 6,5 6,6 6,5 6,3 6,2 2,4 6,2 6,5 6,6 6,5 5,9 2,3 6,2 6,2 6,5 6,6 6,1 2,7 5,9 6,2 6,2 6,5 6,1 2,7 6,1 5,9 6,2 6,2 6,1 2,9 6,1 6,1 5,9 6,2 6,1 3 6,1 6,1 6,1 5,9 6,1 2,2 6,1 6,1 6,1 6,1 6,4 2,3 6,1 6,1 6,1 6,1 6,7 2,8 6,4 6,1 6,1 6,1 6,9 2,8 6,7 6,4 6,1 6,1 7 2,8 6,9 6,7 6,4 6,1 7 2,2 7 6,9 6,7 6,4 6,8 2,6 7 7 6,9 6,7 6,4 2,8 6,8 7 7 6,9 5,9 2,5 6,4 6,8 7 7 5,5 2,4 5,9 6,4 6,8 7 5,5 2,3 5,5 5,9 6,4 6,8 5,6 1,9 5,5 5,5 5,9 6,4 5,8 1,7 5,6 5,5 5,5 5,9 5,9 2 5,8 5,6 5,5 5,5 6,1 2,1 5,9 5,8 5,6 5,5 6,1 1,7 6,1 5,9 5,8 5,6 6 1,8 6,1 6,1 5,9 5,8 6 1,8 6 6,1 6,1 5,9 5,9 1,8 6 6 6,1 6,1 5,5 1,3 5,9 6 6 6,1 5,6 1,3 5,5 5,9 6 6 5,4 1,3 5,6 5,5 5,9 6 5,2 1,2 5,4 5,6 5,5 5,9 5,2 1,4 5,2 5,4 5,6 5,5 5,2 2,2 5,2 5,2 5,4 5,6 5,5 2,9 5,2 5,2 5,2 5,4 5,8 3,1 5,5 5,2 5,2 5,2 5,8 3,5 5,8 5,5 5,2 5,2 5,5 3,6 5,8 5,8 5,5 5,2 5,3 4,4 5,5 5,8 5,8 5,5 5,1 4,1 5,3 5,5 5,8 5,8 5,2 5,1 5,1 5,3 5,5 5,8 5,8 5,8 5,2 5,1 5,3 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WMan>25[t] = + 0.205529147155612 -0.006701733132186Infl[t] + 1.46424310835333`Yt-1`[t] -0.572214153777315`Yt-2`[t] -0.306648555087636`Yt-3`[t] + 0.404540471386374`Yt-4`[t] + 0.00841686847188313M1[t] -0.192488288817357M2[t] -0.133691692405834M3[t] -0.162225291504273M4[t] -0.213984572812024M5[t] -0.354608452344717M6[t] -0.0590469925769761M7[t] -0.43876956278108M8[t] -0.336609775414806M9[t] -0.209948728671440M10[t] -0.200347599504354M11[t] + 0.00233719208955934t + 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) 0.205529147155612 0.627458 0.3276 0.745044 0.372522 Infl -0.006701733132186 0.020618 -0.325 0.746932 0.373466 `Yt-1` 1.46424310835333 0.157152 9.3174 0 0 `Yt-2` -0.572214153777315 0.2819 -2.0298 0.049417 0.024708 `Yt-3` -0.306648555087636 0.283438 -1.0819 0.28612 0.14306 `Yt-4` 0.404540471386374 0.170919 2.3669 0.023138 0.011569 M1 0.00841686847188313 0.120462 0.0699 0.944662 0.472331 M2 -0.192488288817357 0.127934 -1.5046 0.140695 0.070348 M3 -0.133691692405834 0.132805 -1.0067 0.320459 0.160229 M4 -0.162225291504273 0.133475 -1.2154 0.231713 0.115856 M5 -0.213984572812024 0.130341 -1.6417 0.108898 0.054449 M6 -0.354608452344717 0.129565 -2.7369 0.00938 0.00469 M7 -0.0590469925769761 0.129365 -0.4564 0.650674 0.325337 M8 -0.43876956278108 0.127628 -3.4379 0.001436 0.000718 M9 -0.336609775414806 0.140883 -2.3893 0.02195 0.010975 M10 -0.209948728671440 0.127155 -1.6511 0.106954 0.053477 M11 -0.200347599504354 0.123495 -1.6223 0.113004 0.056502 t 0.00233719208955934 0.002109 1.1085 0.274629 0.137315 Multiple Linear Regression - Regression Statistics Multiple R 0.965451375198482 R-squared 0.932096357872639 Adjusted R-squared 0.901718412710399 F-TEST (value) 30.6833247902241 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.172463277800623 Sum Squared Residuals 1.13025612320992 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.5 6.58515908754108 -0.08515908754108 2 6.6 6.55453754831352 0.0454624516864788 3 6.5 6.54385853879865 -0.0438585387986542 4 6.2 6.33024392227036 -0.130243922270363 5 6.2 5.95169424794529 0.248305752054712 6 5.9 6.05686088259597 -0.156860882595968 7 6.1 5.96434642808205 0.135653571917952 8 6.1 5.93011177635545 0.169888223644548 9 6.1 6.01082014495567 0.0891798550443245 10 6.1 5.95645635804194 0.143543641958056 11 6.1 6.05466416008161 0.0453358399183878 12 6.4 6.2566787783623 0.143321221637694 13 6.7 6.70335490486366 -0.00335490486365748 14 6.9 6.77239562603678 0.127604373963219 15 7 6.86271922354905 0.137280776450954 16 7 6.90189291138897 0.0981070886110306 17 6.8 6.85260114393856 -0.0526011439385567 18 6.4 6.47036872696683 -0.0703687269668295 19 5.9 6.33947753331655 -0.439477533316553 20 5.5 5.52085614686701 -0.0208561468670132 21 5.5 5.36818446094117 0.131815539058832 22 5.6 5.72025714352716 -0.120257143527163 23 5.8 5.80034930858745 -0.000349308587445725 24 5.9 6.07483459798009 -0.174834597980089 25 6.1 6.08623510979942 0.0137648902005789 26 6.1 6.10509938026666 -0.00509938026665854 27 6 6.10136340346757 -0.101363403467571 28 6 5.90786702174447 0.0921329782555311 29 5.9 5.99657444218128 -0.0965744421812821 30 5.5 5.74587916597767 -0.245879165977672 31 5.6 5.47484794273273 0.125152057267267 32 5.4 5.50343739247321 -0.103437392473210 33 5.2 5.34073988309028 -0.140739883090282 34 5.2 5.09751094031825 0.102489059681746 35 5.2 5.32031446398078 -0.120314463980777 36 5.5 5.49872965912241 0.00127034087758668 37 5.8 5.86650821128614 -0.0665082112861441 38 5.8 5.93286823920639 -0.132868239206394 39 5.5 5.72967304173477 -0.229673041734773 40 5.3 5.28820989060377 0.0117901093962337 41 5.1 5.24097608720367 -0.140976087203669 42 5.2 5.00957644223944 0.190423557760564 43 5.8 5.50361859209662 0.296381407903381 44 5.8 5.92730910704338 -0.127309107043377 45 5.5 5.58025551101287 -0.0802555110128746 46 5 5.12577555811264 -0.125775558112639 47 4.9 4.82467206735017 0.075327932649835 48 5.3 5.26975696453519 0.0302430354648085 49 6.1 5.9587426865097 0.141257313490303 50 6.5 6.53509920617665 -0.0350992061766451 51 6.8 6.56238579244996 0.237614207550044 52 6.6 6.67178625399243 -0.0717862539924327 53 6.4 6.3581540787312 0.0418459212687959 54 6.4 6.11731478222009 0.282685217779906 55 6.6 6.71770950377205 -0.117709503772046 56 6.7 6.61828557726095 0.0817144227390516 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.531418945737452 0.937162108525097 0.468581054262548 22 0.420735770288982 0.841471540577964 0.579264229711018 23 0.663305654576485 0.67338869084703 0.336694345423515 24 0.75679832714974 0.486403345700519 0.243201672850260 25 0.647019330916226 0.705961338167547 0.352980669083774 26 0.58154623193991 0.83690753612018 0.41845376806009 27 0.47113896236484 0.94227792472968 0.52886103763516 28 0.577203536739751 0.845592926520497 0.422796463260249 29 0.85657481084853 0.28685037830294 0.14342518915147 30 0.791855379951965 0.41628924009607 0.208144620048035 31 0.883315572785402 0.233368854429197 0.116684427214598 32 0.831202943163046 0.337594113673909 0.168797056836954 33 0.734940841180339 0.530118317639323 0.265059158819661 34 0.664558535493557 0.670882929012885 0.335441464506443 35 0.678185020686193 0.643629958627615 0.321814979313807 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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