*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, 18 Nov 2009 09:49:45 -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/18/t12585630836s56gnwu01d6xvi.htm/, Retrieved Wed, 18 Nov 2009 17:51:35 +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/18/t12585630836s56gnwu01d6xvi.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:

ws7autoregr4lagswmanecogr

Dataseries X:

» Textbox « » Textfile « » CSV «

7,60 101,60 7,50 7,70 8,10 8,00 7,80 94,60 7,60 7,50 7,70 8,10 7,80 95,90 7,80 7,60 7,50 7,70 7,80 104,70 7,80 7,80 7,60 7,50 7,50 102,80 7,80 7,80 7,80 7,60 7,50 98,10 7,50 7,80 7,80 7,80 7,10 113,90 7,50 7,50 7,80 7,80 7,50 80,90 7,10 7,50 7,50 7,80 7,50 95,70 7,50 7,10 7,50 7,50 7,60 113,20 7,50 7,50 7,10 7,50 7,70 105,90 7,60 7,50 7,50 7,10 7,70 108,80 7,70 7,60 7,50 7,50 7,90 102,30 7,70 7,70 7,60 7,50 8,10 99,00 7,90 7,70 7,70 7,60 8,20 100,70 8,10 7,90 7,70 7,70 8,20 115,50 8,20 8,10 7,90 7,70 8,20 100,70 8,20 8,20 8,10 7,90 7,90 109,90 8,20 8,20 8,20 8,10 7,30 114,60 7,90 8,20 8,20 8,20 6,90 85,40 7,30 7,90 8,20 8,20 6,60 100,50 6,90 7,30 7,90 8,20 6,70 114,80 6,60 6,90 7,30 7,90 6,90 116,50 6,70 6,60 6,90 7,30 7,00 112,90 6,90 6,70 6,60 6,90 7,10 102,00 7,00 6,90 6,70 6,60 7,20 106,00 7,10 7,00 6,90 6,70 7,10 105,30 7,20 7,10 7,00 6,90 6,90 118,80 7,10 7,20 7,10 7,00 7,00 106,10 6,90 7,10 7,20 7,10 6,80 109,30 7,00 6,90 7,10 7,20 6,40 117,20 6,80 7,00 6,90 7,10 6,70 92, 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.79602878864052 -0.0114001793440848X[t] + 1.51143732820451Y1[t] -0.799982797357693Y2[t] -0.149890180597183Y3[t] + 0.348577798011597Y4[t] + 0.163755712329852M1[t] + 0.0840941126806134M2[t] -0.0646153641388665M3[t] + 0.113569726413263M4[t] + 0.0937133069211612M5[t] -0.0861895999292222M6[t] -0.0149736549364430M7[t] + 0.208290863164784M8[t] -0.445482542571144M9[t] + 0.0385107772688626M10[t] + 0.136504622499525M11[t] + 0.00059177892543175t + 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) 1.79602878864052 1.095451 1.6395 0.109356 0.054678 X -0.0114001793440848 0.005248 -2.1723 0.036137 0.018068 Y1 1.51143732820451 0.140488 10.7585 0 0 Y2 -0.799982797357693 0.277242 -2.8855 0.006408 0.003204 Y3 -0.149890180597183 0.282766 -0.5301 0.599136 0.299568 Y4 0.348577798011597 0.164658 2.117 0.040866 0.020433 M1 0.163755712329852 0.142287 1.1509 0.256969 0.128485 M2 0.0840941126806134 0.144936 0.5802 0.565195 0.282597 M3 -0.0646153641388665 0.143944 -0.4489 0.656059 0.328029 M4 0.113569726413263 0.141304 0.8037 0.426554 0.213277 M5 0.0937133069211612 0.139989 0.6694 0.507266 0.253633 M6 -0.0861895999292222 0.136487 -0.6315 0.531504 0.265752 M7 -0.0149736549364430 0.141393 -0.1059 0.916218 0.458109 M8 0.208290863164784 0.16586 1.2558 0.216847 0.108423 M9 -0.445482542571144 0.166404 -2.6771 0.010903 0.005452 M10 0.0385107772688626 0.169544 0.2271 0.82153 0.410765 M11 0.136504622499525 0.154802 0.8818 0.383427 0.191714 t 0.00059177892543175 0.002824 0.2095 0.835142 0.417571 Multiple Linear Regression - Regression Statistics Multiple R 0.96849898486634 R-squared 0.937990283687128 Adjusted R-squared 0.910249094810317 F-TEST (value) 33.812187640999 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.195680862179208 Sum Squared Residuals 1.45505799328153 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.6 7.55254240167197 0.0474575983280287 2 7.8 7.9592279806888 -0.159227980688793 3 7.8 7.90912615246737 -0.109126152467365 4 7.8 7.7428803065834 0.057119693416598 5 7.5 7.75015575045222 -0.250155750452216 6 7.5 7.24070982658543 0.259290173414571 7 7.1 7.37238955607441 -0.272389556074408 8 7.5 7.41284389435322 0.0871561056467839 9 7.5 7.41093432407167 0.089065675928332 10 7.6 7.43597923761142 0.164020762388583 11 7.7 7.56954271235627 0.130457287643732 12 7.7 7.61114592097365 0.0888540790263492 13 7.9 7.75460728017 0.145392719830002 14 8.1 8.03531427866402 0.0646857213359837 15 8.2 8.04496496185554 0.155035038144454 16 8.2 8.01618831427013 0.183811685729872 17 8.2 8.12538557174303 0.0746144282569725 18 7.9 7.8959193353951 0.00408066460490439 19 7.3 7.49557279773592 -0.195572797735916 20 6.9 7.38544677389445 -0.485446773894451 21 6.6 6.48050424030024 0.119495759699759 22 6.7 6.65398946388182 0.0460105361181818 23 6.9 6.97514274861264 -0.0751427486126431 24 7 7.0080956715569 -0.0080956715569044 25 7.1 7.16828993354843 -0.0682899335484273 26 7.2 7.11964459221469 0.0803554077853144 27 7.1 7.10537901448878 -0.00537901448878178 28 6.9 6.91898021200642 -0.0189802120064168 29 7 6.84207742494593 0.157922575054066 30 6.8 6.98727281327278 -0.187272813272778 31 6.4 6.58185363131432 -0.181853631314323 32 6.7 6.55801140866758 0.141988591332424 33 6.6 6.60970781685631 -0.00970781685631363 34 6.4 6.59877336767464 -0.19877336767464 35 6.3 6.17780985703537 0.122190142964630 36 6.2 6.27405382960673 -0.0740538296067317 37 6.5 6.51399850937194 -0.0139985093719392 38 6.8 6.79164970632095 0.00835029367905362 39 6.8 6.81315922931692 -0.0131592293169240 40 6.4 6.70631696363912 -0.306316963639117 41 6.1 6.05658233193433 0.0434176680656684 42 5.8 5.94188793451608 -0.141887934516077 43 6.1 5.78269415187934 0.317305848120661 44 7.2 6.83237599049646 0.367624009503536 45 7.3 7.49885361877178 -0.198853618771777 46 6.9 6.91125793083213 -0.0112579308321255 47 6.1 6.27750468199572 -0.177504681995719 48 5.8 5.80670457786271 -0.00670457786271334 49 6.2 6.31056187523766 -0.110561875237664 50 7.1 7.09416344211156 0.00583655788844133 51 7.7 7.72737064187138 -0.0273706418713827 52 7.9 7.81563420350094 0.0843657964990638 53 7.7 7.72579892092449 -0.0257989209244906 54 7.4 7.33421009023062 0.0657899097693797 55 7.5 7.16748986299601 0.332510137003986 56 8 8.1113219325883 -0.111321932588294 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.874923694466218 0.250152611067563 0.125076305533782 22 0.780459623698999 0.439080752602002 0.219540376301001 23 0.685960775894391 0.628078448211218 0.314039224105609 24 0.589635830533232 0.820728338933536 0.410364169466768 25 0.547978548478104 0.904042903043792 0.452021451521896 26 0.458827060749577 0.917654121499154 0.541172939250423 27 0.333875591652137 0.667751183304274 0.666124408347863 28 0.254472854226383 0.508945708452766 0.745527145773617 29 0.313113056834220 0.626226113668439 0.68688694316578 30 0.225917242000888 0.451834484001777 0.774082757999112 31 0.332296073216998 0.664592146433996 0.667703926783002 32 0.331736325083359 0.663472650166718 0.668263674916641 33 0.388577624836326 0.777155249672651 0.611422375163674 34 0.334921561502185 0.66984312300437 0.665078438497815 35 0.6249029661222 0.7501940677556 0.3750970338778 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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