4 lag

*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: Thu, 19 Nov 2009 13:53:48 -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/19/t1258664137yd0vzcgr1g7w59c.htm/, Retrieved Thu, 19 Nov 2009 21:55:49 +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/19/t1258664137yd0vzcgr1g7w59c.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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0 6.5 6.3 6.1 6.2 6.3 0 6.6 6.5 6.3 6.1 6.2 0 6.5 6.6 6.5 6.3 6.1 0 6.2 6.5 6.6 6.5 6.3 0 6.2 6.2 6.5 6.6 6.5 0 5.9 6.2 6.2 6.5 6.6 0 6.1 5.9 6.2 6.2 6.5 0 6.1 6.1 5.9 6.2 6.2 0 6.1 6.1 6.1 5.9 6.2 0 6.1 6.1 6.1 6.1 5.9 0 6.1 6.1 6.1 6.1 6.1 0 6.4 6.1 6.1 6.1 6.1 0 6.7 6.4 6.1 6.1 6.1 0 6.9 6.7 6.4 6.1 6.1 0 7 6.9 6.7 6.4 6.1 0 7 7 6.9 6.7 6.4 0 6.8 7 7 6.9 6.7 0 6.4 6.8 7 7 6.9 0 5.9 6.4 6.8 7 7 0 5.5 5.9 6.4 6.8 7 0 5.5 5.5 5.9 6.4 6.8 0 5.6 5.5 5.5 5.9 6.4 0 5.8 5.6 5.5 5.5 5.9 0 5.9 5.8 5.6 5.5 5.5 0 6.1 5.9 5.8 5.6 5.5 0 6.1 6.1 5.9 5.8 5.6 0 6 6.1 6.1 5.9 5.8 0 6 6 6.1 6.1 5.9 0 5.9 6 6 6.1 6.1 0 5.5 5.9 6 6 6.1 0 5.6 5.5 5.9 6 6 0 5.4 5.6 5.5 5.9 6 0 5.2 5.4 5.6 5.5 5.9 0 5.2 5.2 5.4 5.6 5.5 0 5.2 5.2 5.2 5.4 5.6 0 5.5 5.2 5.2 5.2 5.4 1 5.8 5.5 5.2 5.2 5.2 1 5.8 5.8 5.5 5.2 5.2 1 5.5 5.8 5.8 5.5 5.2 1 5.3 5.5 5.8 5.8 5.5 1 5.1 5.3 5.5 5.8 5.8 1 5.2 5.1 5.3 5.5 5.8 1 5.8 5.2 5.1 5.3 5.5 1 5.8 5.8 5.2 5.1 5.3 1 5.5 5.8 5.8 5.2 5.1 1 5 5.5 5.8 5.8 5.2 1 4.9 5 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 y[t] = -0.0346622960368248 + 0.0589758078691045x[t] + 1.50682864869239y1[t] -0.632805983146732y2[t] -0.275699725509361y3[t] + 0.431531623605503y4[t] -0.0126969934258707M1[t] -0.209114897281531M2[t] -0.142221133838311M3[t] -0.178080352483085M4[t] -0.238176192560859M5[t] -0.383383749504528M6[t] -0.0469800234484245M7[t] -0.488027705147431M8[t] -0.340348596260656M9[t] -0.213105342498909M10[t] -0.202673655015069M11[t] + 0.00164230830510336t + 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) -0.0346622960368248 0.620921 -0.0558 0.955791 0.477895 x 0.0589758078691045 0.094445 0.6244 0.536273 0.268137 y1 1.50682864869239 0.16233 9.2825 0 0 y2 -0.632805983146732 0.294958 -2.1454 0.038738 0.019369 y3 -0.275699725509361 0.299869 -0.9194 0.364007 0.182003 y4 0.431531623605503 0.186137 2.3184 0.026223 0.013112 M1 -0.0126969934258707 0.124226 -0.1022 0.919158 0.459579 M2 -0.209114897281531 0.131705 -1.5877 0.121089 0.060544 M3 -0.142221133838311 0.135794 -1.0473 0.301929 0.150964 M4 -0.178080352483085 0.135795 -1.3114 0.19803 0.099015 M5 -0.238176192560859 0.134072 -1.7765 0.084106 0.042053 M6 -0.383383749504528 0.134458 -2.8513 0.007165 0.003583 M7 -0.0469800234484245 0.13453 -0.3492 0.728962 0.364481 M8 -0.488027705147431 0.132214 -3.6912 0.000734 0.000367 M9 -0.340348596260656 0.144005 -2.3635 0.023624 0.011812 M10 -0.213105342498909 0.12887 -1.6536 0.106895 0.053448 M11 -0.202673655015069 0.124838 -1.6235 0.11321 0.056605 t 0.00164230830510336 0.003143 0.5225 0.604525 0.302263 Multiple Linear Regression - Regression Statistics Multiple R 0.96454395128867 R-squared 0.93034503396756 Adjusted R-squared 0.897452411118909 F-TEST (value) 28.2843067349277 F-TEST (DF numerator) 17 F-TEST (DF denominator) 36 p-value 7.7715611723761e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.174263106623220 Sum Squared Residuals 1.09323469187913 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.5 6.59649793896602 -0.0964979389660187 2 6.6 6.56094368671497 0.0390563132850288 3 6.5 6.55530831924076 -0.0553083192407632 4 6.2 6.33829432533641 -0.138294325336408 5 6.2 5.94980914944086 0.250190850559141 6 5.9 6.0668088306578 -0.166808830657799 7 6.1 5.99236302570355 0.107636974296451 8 6.1 5.91470568991049 0.185294310089509 9 6.1 6.02017582812583 0.0798241718741687 10 6.1 5.96446195800916 0.135538041990841 11 6.1 6.0628422785192 0.0371577214807976 12 6.4 6.26715824183937 0.132841758160626 13 6.7 6.70815215132632 -0.00815215132632399 14 6.9 6.77558335543946 0.124416644560537 15 7 6.87293344432944 0.127066555670564 16 7 6.9095877716585 0.0904122283415 17 6.8 6.86217318355093 -0.0621731835509351 18 6.4 6.47597855734406 -0.0759785573440556 19 5.9 6.38100749121821 -0.481007491218206 20 5.5 5.49645013183867 0.00354986816132527 21 5.5 5.38341664660961 0.116583353390393 22 5.6 5.73066181524763 -0.13066181524763 23 5.8 5.7879327543068 0.0120672456931957 24 5.9 6.05772119960858 -0.157721199608579 25 6.1 6.04321821017677 0.0567817898232305 26 6.1 6.07454096330869 0.0254590366913063 27 6 6.07525219059784 -0.075252190597835 28 6 5.8783656326476 0.121634367352395 29 5.9 5.96949902391071 -0.0694990239107069 30 5.5 5.70282088295384 -0.202820882953839 31 5.6 5.45826289379221 0.141737106207786 32 5.4 5.45023275107718 -0.0502327510771779 33 5.2 5.3020345680591 -0.102034568059102 34 5.2 5.05593297502368 0.144067024976317 35 5.2 5.2928612749044 -0.0928612749043944 36 5.5 5.46601085860534 0.0339891413946611 37 5.8 5.87967425124029 -0.0796742512402913 38 5.8 5.94710545535343 -0.147105455353431 39 5.5 5.74308981450493 -0.243089814504926 40 5.3 5.30357387898638 -0.00357387898638284 41 5.1 5.2630558995009 -0.163055899500905 42 5.2 5.02739603540602 0.172603964593985 43 5.8 5.56836658928603 0.231633410713970 44 5.8 5.93861142717366 -0.138611427173657 45 5.5 5.59437295720546 -0.0943729572054596 46 5 5.14894325171953 -0.148943251719528 47 4.9 4.8563636922696 0.043636307730401 48 5.3 5.30910969994671 -0.00910969994670775 49 6.1 5.9724574482906 0.127542551709403 50 6.5 6.54182653918344 -0.0418265391834409 51 6.8 6.55341623132704 0.246583768672960 52 6.6 6.6701783913711 -0.070178391371104 53 6.4 6.3554627435966 0.0445372564034061 54 6.4 6.12699569363829 0.273004306361709 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.86079724994665 0.278405500106701 0.139202750053350 22 0.816399208721522 0.367201582556955 0.183600791278478 23 0.813820834029729 0.372358331940542 0.186179165970271 24 0.895529752167374 0.208940495665251 0.104470247832626 25 0.831519100812905 0.33696179837419 0.168480899187095 26 0.804417182977151 0.391165634045698 0.195582817022849 27 0.703922111633623 0.592155776732755 0.296077888366378 28 0.698365639199375 0.60326872160125 0.301634360800625 29 0.691525026063976 0.616949947872048 0.308474973936024 30 0.721648994756723 0.556702010486554 0.278351005243277 31 0.73019769261714 0.53960461476572 0.26980230738286 32 0.590892394428852 0.818215211142295 0.409107605571148 33 0.467412592136979 0.934825184273957 0.532587407863021 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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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