*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 10:36:35 -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/t1258739871adavkx60fmo0b0q.htm/, Retrieved Fri, 20 Nov 2009 18:58:03 +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/t1258739871adavkx60fmo0b0q.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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8 5560 0 0 0 0 8.1 3922 8 0 0 0 7.7 3759 8.1 8 0 0 7.5 4138 7.7 8.1 8 0 7.6 4634 7.5 7.7 8.1 8 7.8 3996 7.6 7.5 7.7 8.1 7.8 4308 7.8 7.6 7.5 7.7 7.8 4143 7.8 7.8 7.6 7.5 7.5 4429 7.8 7.8 7.8 7.6 7.5 5219 7.5 7.8 7.8 7.8 7.1 4929 7.5 7.5 7.8 7.8 7.5 5755 7.1 7.5 7.5 7.8 7.5 5592 7.5 7.1 7.5 7.5 7.6 4163 7.5 7.5 7.1 7.5 7.7 4962 7.6 7.5 7.5 7.1 7.7 5208 7.7 7.6 7.5 7.5 7.9 4755 7.7 7.7 7.6 7.5 8.1 4491 7.9 7.7 7.7 7.6 8.2 5732 8.1 7.9 7.7 7.7 8.2 5731 8.2 8.1 7.9 7.7 8.2 5040 8.2 8.2 8.1 7.9 7.9 6102 8.2 8.2 8.2 8.1 7.3 4904 7.9 8.2 8.2 8.2 6.9 5369 7.3 7.9 8.2 8.2 6.7 5578 6.9 7.3 7.9 8.2 6.7 4619 6.7 6.9 7.3 7.9 6.9 4731 6.7 6.7 6.9 7.3 7 5011 6.9 6.7 6.7 6.9 7.1 5299 7 6.9 6.7 6.7 7.2 4146 7.1 7 6.9 6.7 7.1 4625 7.2 7.1 7 6.9 6.9 4736 7.1 7.2 7.1 7 7 4219 6.9 7.1 7.2 7.1 6.8 5116 7 6.9 7.1 7.2 6.4 4205 6.8 7 6.9 7.1 6.7 4121 6.4 6.8 7 6.9 6.6 5103 6.7 6.4 6.8 7 6.4 4300 6.6 6.7 6.4 6.8 6.3 4578 6.4 6.6 6.7 6.4 6.2 3809 6.3 6.4 6.6 6.7 6.5 5526 6.2 6.3 6.4 6.6 6.8 4247 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 6.45334600611849 + 2.86270785610798e-05X[t] + 0.313663967704978Y1[t] -0.0391313044914567Y2[t] -0.0475363981301766Y3[t] -0.0511292781289009Y4[t] + 0.0976468238655872M1[t] -0.587691273323679M2[t] -0.691345384808646M3[t] -0.634225040597112M4[t] -0.31093127283165M5[t] -0.0254784574698382M6[t] -0.0183527603020163M7[t] -0.0976254621655117M8[t] -0.166708756365665M9[t] -0.324682647520785M10[t] -0.434249952247223M11[t] -0.0133276870234248t + 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) 6.45334600611849 1.009816 6.3906 0 0 X 2.86270785610798e-05 0.000163 0.1756 0.861413 0.430707 Y1 0.313663967704978 0.096369 3.2548 0.002215 0.001107 Y2 -0.0391313044914567 0.106875 -0.3661 0.716056 0.358028 Y3 -0.0475363981301766 0.106688 -0.4456 0.658148 0.329074 Y4 -0.0511292781289009 0.079544 -0.6428 0.523782 0.261891 M1 0.0976468238655872 0.355687 0.2745 0.784992 0.392496 M2 -0.587691273323679 0.384 -1.5304 0.133231 0.066615 M3 -0.691345384808646 0.378884 -1.8247 0.075 0.0375 M4 -0.634225040597112 0.375584 -1.6886 0.09853 0.049265 M5 -0.31093127283165 0.354505 -0.8771 0.385314 0.192657 M6 -0.0254784574698382 0.364483 -0.0699 0.944595 0.472298 M7 -0.0183527603020163 0.357641 -0.0513 0.959311 0.479656 M8 -0.0976254621655117 0.358981 -0.272 0.786961 0.39348 M9 -0.166708756365665 0.357814 -0.4659 0.643632 0.321816 M10 -0.324682647520785 0.35839 -0.9059 0.370012 0.185006 M11 -0.434249952247223 0.353522 -1.2284 0.225995 0.112998 t -0.0133276870234248 0.005246 -2.5404 0.014766 0.007383 Multiple Linear Regression - Regression Statistics Multiple R 0.700175703647055 R-squared 0.490246015977649 Adjusted R-squared 0.288715371131603 F-TEST (value) 2.43261274905442 F-TEST (DF numerator) 17 F-TEST (DF denominator) 43 p-value 0.00948963500605382 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.557968541564462 Sum Squared Residuals 13.3871424151496 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8 6.69683169976024 1.30316830023976 2 8.1 8.46058650250434 -0.36058650250434 3 7.7 8.05725445102933 -0.357254451029332 4 7.5 7.60222686841954 -0.102226868419543 5 7.6 7.46552384353924 0.13447615646076 6 7.8 7.77247918486363 0.0275208151363730 7 7.8 7.86398749748853 -0.0639874974885262 8 7.8 7.7643095955535 0.0356904044465012 9 7.5 7.67546575135946 -0.175465751359464 10 7.5 7.4224545193069 0.0775454806930998 11 7.1 7.30299706612176 -0.202997066121761 12 7.5 7.63636063059407 -0.136360630594072 13 7.5 7.87247044594802 -0.372470445948023 14 7.6 7.13625860392704 0.463741396072962 15 7.7 7.07495338995893 0.625046610041066 16 7.7 7.13278986354286 0.567210136457139 17 7.9 7.42112110743457 0.478878892565434 18 8.1 7.73855491294792 0.361445087052084 19 8.2 7.81767273241643 0.382327267583572 20 8.2 7.73907657269712 0.460923427302882 21 8.2 7.61323801448687 0.586761985513128 22 7.9 7.4573588983014 0.442641101698604 23 7.3 7.20095654831098 0.0990434516890234 24 6.9 7.45873141579013 -0.558731415790127 25 6.7 7.46130772710349 -0.761307727103491 26 6.7 6.73196892512309 -0.0319689251230881 27 6.9 6.67571174644124 0.224288253558761 28 7 6.82021177004504 0.179788229954959 29 7.1 7.17218844091066 -0.0721884409106568 30 7.2 7.42925253436344 -0.229252534363435 31 7.1 7.44923668602114 -0.349236686021144 32 6.9 7.31466780800895 -0.414667808008952 33 7 7.14877039645154 -0.148770396451538 34 6.8 7.0419806774112 -0.241980677411199 35 6.4 6.84098070054098 -0.440980700540977 36 6.7 7.1473311807947 -0.447331180794707 37 6.6 7.37390817270507 -0.773908172705071 38 6.4 6.63838947116775 -0.238389471167749 39 6.3 6.47673712922 -0.176737129219994 40 6.2 6.46439028349677 -0.264390283496774 41 6.5 6.81067599924576 -0.310675999245759 42 6.8 7.15917891030396 -0.359178910303962 43 6.8 7.23326579527835 -0.433265795278353 44 6.4 7.13592369572628 -0.735923695726281 45 6.1 6.91081432248138 -0.810814322481376 46 5.8 6.63378980058928 -0.83378980058928 47 6.1 6.4521299016972 -0.352129901697204 48 7.2 7.00034904189677 0.199650958103235 49 7.3 7.46725428479471 -0.167254284794713 50 6.9 6.73279649727778 0.167203502722216 51 6.1 6.4153432833505 -0.315343283350501 52 5.8 6.18038121449578 -0.380381214495782 53 6.2 6.43049060886978 -0.230490608869778 54 7.1 6.90053445752106 0.199465542478940 55 7.7 7.23583728879555 0.46416271120445 56 7.9 7.24602232801415 0.65397767198585 57 7.7 7.15171151522075 0.54828848477925 58 7.4 6.84441610439123 0.555583895608774 59 7.5 6.60293578332908 0.897064216670918 60 8 7.05722773092433 0.94277226907567 61 8.1 7.32822766968846 0.771772330311541 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.352557217605342 0.705114435210684 0.647442782394658 22 0.203679082961054 0.407358165922107 0.796320917038946 23 0.122844693637471 0.245689387274943 0.877155306362529 24 0.720372730835962 0.559254538328077 0.279627269164038 25 0.942750995311777 0.114498009376445 0.0572490046882226 26 0.986673544466686 0.0266529110666276 0.0133264555333138 27 0.979040611942034 0.0419187761159323 0.0209593880579662 28 0.964673741583314 0.0706525168333715 0.0353262584166857 29 0.963244333687943 0.0735113326241147 0.0367556663120573 30 0.938347204651562 0.123305590696876 0.061652795348438 31 0.90035444321857 0.199291113562860 0.0996455567814301 32 0.85933773282444 0.281324534351121 0.140662267175561 33 0.871409642702426 0.257180714595149 0.128590357297574 34 0.797278346467396 0.405443307065208 0.202721653532604 35 0.860241250525368 0.279517498949264 0.139758749474632 36 0.875795297377529 0.248409405244942 0.124204702622471 37 0.8753871156419 0.249225768716199 0.124612884358099 38 0.803812534967014 0.392374930065972 0.196187465032986 39 0.849642372627204 0.300715254745591 0.150357627372796 40 0.873516560460542 0.252966879078916 0.126483439539458 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 2 0.1 NOK 10% type I error level 4 0.2 NOK

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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