*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: Tue, 15 Dec 2009 07:41:53 -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/Dec/15/t12608881927m8zkp7ldaby59r.htm/, Retrieved Tue, 15 Dec 2009 15:43:24 +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/Dec/15/t12608881927m8zkp7ldaby59r.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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24 0 26 27 29 27 30 0 24 26 27 29 26 0 30 24 26 27 28 0 26 30 24 26 28 0 28 26 30 24 24 0 28 28 26 30 23 0 24 28 28 26 24 0 23 24 28 28 24 0 24 23 24 28 27 0 24 24 23 24 28 0 27 24 24 23 25 0 28 27 24 24 19 0 25 28 27 24 19 0 19 25 28 27 19 0 19 19 25 28 20 0 19 19 19 25 16 0 20 19 19 19 22 0 16 20 19 19 21 0 22 16 20 19 25 0 21 22 16 20 29 0 25 21 22 16 28 0 29 25 21 22 25 0 28 29 25 21 26 0 25 28 29 25 24 0 26 25 28 29 28 0 24 26 25 28 28 0 28 24 26 25 28 0 28 28 24 26 28 0 28 28 28 24 32 0 28 28 28 28 31 0 32 28 28 28 22 0 31 32 28 28 29 0 22 31 32 28 31 0 29 22 31 32 29 0 31 29 22 31 32 0 29 31 29 22 32 0 32 29 31 29 31 0 32 32 29 31 29 0 31 32 32 29 28 0 29 31 32 32 28 0 28 29 31 32 29 0 28 28 29 31 22 0 29 28 28 29 26 0 22 29 28 28 24 0 26 22 29 28 27 0 24 26 22 29 27 0 27 24 26 22 23 0 27 27 24 26 21 0 23 27 27 24 19 0 21 23 27 27 17 0 19 21 23 27 19 0 17 19 21 23 21 1 19 17 19 21 13 1 21 19 17 19 8 1 13 21 19 17 5 1 8 13 21 19 10 1 5 8 13 21 6 1 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] = + 7.61004831470845 -3.75078608443637X[t] + 0.714124077615186Y1[t] + 0.0422973984521496Y2[t] + 0.050619872044836Y3[t] -0.108570315495621Y4[t] + 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) 7.61004831470845 3.041613 2.502 0.015048 0.007524 X -3.75078608443637 1.814887 -2.0667 0.043017 0.021508 Y1 0.714124077615186 0.127444 5.6034 1e-06 0 Y2 0.0422973984521496 0.157438 0.2687 0.789097 0.394549 Y3 0.050619872044836 0.156846 0.3227 0.747999 0.374 Y4 -0.108570315495621 0.129587 -0.8378 0.405403 0.202701 Multiple Linear Regression - Regression Statistics Multiple R 0.897253770107216 R-squared 0.805064327971613 Adjusted R-squared 0.789085994198794 F-TEST (value) 50.3847484611405 F-TEST (DF numerator) 5 F-TEST (DF denominator) 61 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.21591846105319 Sum Squared Residuals 630.870024436706 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 25.8558818618298 -1.85588186182976 2 30 24.0669559330664 5.93304406693364 3 26 28.4336263607996 -2.4336263607996 4 28 25.8382450124577 2.16175498754231 5 28 27.6181634371397 0.381836562860281 6 24 26.8488568528909 -2.84885685289095 7 23 24.5278815485024 -1.52788154850236 8 24 23.4274272460873 0.572572753912669 9 24 23.8967744370710 0.103225562928976 10 27 24.3227332254608 2.67726677453918 11 28 26.6242956458468 1.37570435415316 12 25 27.3567416033229 -2.35674160332285 13 19 25.4085263850640 -6.40852638506395 14 19 20.7217986495744 -1.72179864957435 15 19 20.2075843272313 -1.20758432723133 16 20 20.2295760414492 -0.229576041449177 17 16 21.5951220120381 -5.59512201203809 18 22 18.7809231000295 3.21907689997050 19 21 22.9470978439569 -1.94709784395685 20 25 22.1757083533796 2.8242916466204 21 29 25.7279077596397 3.27209224036031 22 28 28.0515518988905 -0.0515518988904749 23 25 27.8176672187589 -2.81766721875885 24 26 25.401195813658 0.598804186341998 25 24 25.5035265618894 -1.50352656188942 26 28 24.0742865044723 3.92571349552769 27 28 27.2225188365605 0.777481163439545 28 28 27.1818983707838 0.81810162921624 29 28 27.6015184899543 0.398481510045653 30 32 27.1672372279719 4.83276277202814 31 31 30.0237335384326 0.97626646156739 32 22 29.478799054626 -7.47879905462602 33 29 23.2118644458165 5.78813555418346 34 31 27.3451552690262 3.65484473097383 35 29 28.7224766805137 0.277523319486308 36 32 28.7102952659621 3.28970473403794 37 32 30.1093202375236 1.89067976247635 38 31 29.9178320577992 1.08216794220082 39 29 29.5727082273097 -0.572708227309743 40 28 27.7764517271404 0.223548272859644 41 28 26.927112980576 1.07288701942397 42 29 26.8921461535298 2.10785384647017 43 22 27.7727909900914 -5.77279099009143 44 26 22.9247901607329 3.07520983926711 45 24 25.5358245540734 -1.53582455407343 46 27 23.8138565728422 3.18614342715782 47 27 26.8341057054321 0.165894294567868 48 23 26.4254768947164 -3.42547689471642 49 21 23.9379808313814 -2.93798083138143 50 19 22.0148321358556 -3.01483213585559 51 17 20.2995096955416 -3.29950969554158 52 19 19.1197082612997 -0.119708261299718 53 21 16.828476422091 4.17152357790901 54 13 18.4572202611272 -5.45722026112724 55 8 13.1472028121910 -5.14720281219096 56 5 9.12230234959626 -4.12230234959626 57 10 6.14634351714002 3.85365648285998 58 6 10.2055348736003 -4.20553487360029 59 6 7.9515175167439 -1.95151751674389 60 8 8.36113822964634 -0.361138229646340 61 11 9.04405531921926 1.95594468078074 62 12 11.7053036109516 0.294696389048393 63 13 12.6475596280129 0.352440371987086 64 19 13.3387000892235 5.66129991077649 65 19 17.3906508789248 1.60934912107524 66 18 17.5864848261869 0.413515173813132 67 20 17.0675096653451 2.93249033465492 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.733678519096941 0.532642961806118 0.266321480903059 10 0.590846353795609 0.818307292408782 0.409153646204391 11 0.446846506397071 0.893693012794143 0.553153493602929 12 0.374716746986471 0.749433493972942 0.625283253013529 13 0.674791686709847 0.650416626580307 0.325208313290153 14 0.64780078786614 0.704398424267721 0.352199212133860 15 0.612657207901543 0.774685584196915 0.387342792098457 16 0.52865365587353 0.94269268825294 0.47134634412647 17 0.575639030370404 0.848721939259192 0.424360969629596 18 0.639403804299275 0.721192391401449 0.360596195700725 19 0.565302089001956 0.869395821996089 0.434697910998044 20 0.521771889590996 0.956456220818009 0.478228110409004 21 0.571014814185708 0.857970371628583 0.428985185814292 22 0.485202484840171 0.970404969680342 0.514797515159829 23 0.451117590729330 0.902235181458661 0.54888240927067 24 0.381162822445913 0.762325644891825 0.618837177554087 25 0.313753903328784 0.627507806657567 0.686246096671216 26 0.340961427457755 0.681922854915509 0.659038572542245 27 0.282472241224323 0.564944482448646 0.717527758775677 28 0.221823045998794 0.443646091997588 0.778176954001206 29 0.171520371123542 0.343040742247084 0.828479628876458 30 0.237864407054014 0.475728814108028 0.762135592945986 31 0.186063653437431 0.372127306874863 0.813936346562569 32 0.447093387540473 0.894186775080946 0.552906612459527 33 0.59800247381181 0.80399505237638 0.40199752618819 34 0.606007227165576 0.787985545668847 0.393992772834424 35 0.531198149936122 0.937603700127756 0.468801850063878 36 0.53958510220075 0.9208297955985 0.46041489779925 37 0.489290672249161 0.978581344498321 0.510709327750839 38 0.420849868276945 0.84169973655389 0.579150131723055 39 0.349493047153248 0.698986094306496 0.650506952846752 40 0.285569634644858 0.571139269289717 0.714430365355142 41 0.237902613727953 0.475805227455905 0.762097386272047 42 0.219963382040656 0.439926764081312 0.780036617959344 43 0.311500936683232 0.623001873366464 0.688499063316768 44 0.358134825795116 0.716269651590231 0.641865174204884 45 0.292871604292398 0.585743208584796 0.707128395707602 46 0.370734464786852 0.741468929573705 0.629265535213148 47 0.29623750538095 0.5924750107619 0.70376249461905 48 0.250366669128781 0.500733338257562 0.749633330871219 49 0.203592819781495 0.40718563956299 0.796407180218505 50 0.166338539771046 0.332677079542092 0.833661460228954 51 0.139824411433458 0.279648822866915 0.860175588566543 52 0.0922688712011222 0.184537742402244 0.907731128798878 53 0.11000933382014 0.22001866764028 0.88999066617986 54 0.179458518960812 0.358917037921624 0.820541481039188 55 0.223572927040154 0.447145854080308 0.776427072959846 56 0.397355897181642 0.794711794363285 0.602644102818358 57 0.446543169484933 0.893086338969866 0.553456830515067 58 0.499576677758224 0.999153355516448 0.500423322241776 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):

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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