*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 11:33:48 -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/20/t1258742440ppytnwgw8ezac04.htm/, Retrieved Fri, 20 Nov 2009 19:40:53 +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/t1258742440ppytnwgw8ezac04.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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0,2 1 0,6 0 1,9 3,2 0,9 1 0,2 0,6 0 1,9 2,4 1 0,9 0,2 0,6 0 4,7 1 2,4 0,9 0,2 0,6 9,4 1 4,7 2,4 0,9 0,2 12,5 1 9,4 4,7 2,4 0,9 15,8 1 12,5 9,4 4,7 2,4 18,2 1 15,8 12,5 9,4 4,7 16,8 0 18,2 15,8 12,5 9,4 17,3 0 16,8 18,2 15,8 12,5 19,3 0 17,3 16,8 18,2 15,8 17,9 0 19,3 17,3 16,8 18,2 20,2 0 17,9 19,3 17,3 16,8 18,7 0 20,2 17,9 19,3 17,3 20,1 0 18,7 20,2 17,9 19,3 18,2 0 20,1 18,7 20,2 17,9 18,4 0 18,2 20,1 18,7 20,2 18,2 0 18,4 18,2 20,1 18,7 18,9 0 18,2 18,4 18,2 20,1 19,9 0 18,9 18,2 18,4 18,2 21,3 0 19,9 18,9 18,2 18,4 20 0 21,3 19,9 18,9 18,2 19,5 0 20 21,3 19,9 18,9 19,6 0 19,5 20 21,3 19,9 20,9 0 19,6 19,5 20 21,3 21 0 20,9 19,6 19,5 20 19,9 0 21 20,9 19,6 19,5 19,6 0 19,9 21 20,9 19,6 20,9 0 19,6 19,9 21 20,9 21,7 0 20,9 19,6 19,9 21 22,9 0 21,7 20,9 19,6 19,9 21,5 0 22,9 21,7 20,9 19,6 21,3 0 21,5 22,9 21,7 20,9 23,5 0 21,3 21,5 22,9 21,7 21,6 0 23,5 21,3 21,5 22,9 24,5 0 21,6 23,5 21,3 21,5 22,2 0 24,5 21,6 23,5 21,3 23,5 0 22,2 24,5 21,6 23,5 20,9 0 23,5 22,2 24,5 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] = + 0.519647105611932 + 1.28632287139419X[t] + 0.92813262756989Y1[t] + 0.336764561898729Y2[t] -0.439355918249917Y3[t] + 0.115147021620269Y4[t] + 0.182944690656144M1[t] + 0.332354786967214M2[t] + 0.351787973684101M3[t] + 0.236941355263420M4[t] + 0.445899792676542M5[t] + 0.6150272299015M6[t] + 0.59084113843511M7[t] + 0.333801824039458M8[t] + 0.49230003939364M9[t] + 0.912247008553877M10[t] + 0.618871180476981M11[t] + 0.00823090323162158t + 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) 0.519647105611932 2.087843 0.2489 0.804785 0.402392 X 1.28632287139419 1.823485 0.7054 0.484851 0.242425 Y1 0.92813262756989 0.16089 5.7688 1e-06 1e-06 Y2 0.336764561898729 0.202726 1.6612 0.104908 0.052454 Y3 -0.439355918249917 0.205414 -2.1389 0.038933 0.019466 Y4 0.115147021620269 0.152488 0.7551 0.454831 0.227415 M1 0.182944690656144 1.142351 0.1601 0.873613 0.436807 M2 0.332354786967214 1.139071 0.2918 0.772044 0.386022 M3 0.351787973684101 1.134906 0.31 0.758277 0.379138 M4 0.236941355263420 1.133238 0.2091 0.8355 0.41775 M5 0.445899792676542 1.13587 0.3926 0.696836 0.348418 M6 0.6150272299015 1.140329 0.5393 0.592797 0.296399 M7 0.59084113843511 1.146563 0.5153 0.609318 0.304659 M8 0.333801824039458 1.156665 0.2886 0.774464 0.387232 M9 0.49230003939364 1.191888 0.413 0.681897 0.340949 M10 0.912247008553877 1.187457 0.7682 0.447095 0.223548 M11 0.618871180476981 1.18309 0.5231 0.603944 0.301972 t 0.00823090323162158 0.018177 0.4528 0.653248 0.326624 Multiple Linear Regression - Regression Statistics Multiple R 0.964983665084489 R-squared 0.931193473879893 Adjusted R-squared 0.900411606931424 F-TEST (value) 30.2513643970582 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.67073379959745 Sum Squared Residuals 106.071354306458 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.2 2.08771937194585 -1.88771937194584 2 0.9 2.76125117416827 -1.86125117416827 3 2.4 2.82150938662777 -0.421509386627771 4 4.7 4.58765838639479 0.112341613605212 5 9.4 7.09109166187532 2.30890833812468 6 12.5 11.8268008820368 0.673199117963227 7 15.8 15.4330522006483 0.366947799351721 8 18.2 17.4909169363030 0.709083063697043 9 16.8 18.8893521989686 -2.08935219896863 10 17.3 17.7334605781177 -0.433460578117702 11 19.3 16.7664425479462 2.53355745205376 12 17.9 19.0719009442286 -1.17190094422856 13 20.2 18.2563361939226 1.94366380607740 14 18.7 19.2560735245281 -0.556073524528114 15 20.1 19.5114894942793 0.588510505720713 16 18.2 19.0273881725968 -0.827388172596795 17 18.4 18.8764679346185 -0.476467934618465 18 18.2 17.8117813150011 0.388218684998854 19 18.9 18.6735345885754 0.226465411424633 20 19.9 18.700415579602 1.19958442039798 21 21.3 20.1419131070609 1.15808689293914 22 20 21.8756626728503 -1.87566267285030 23 19.5 20.4966627157067 -0.996662715706658 24 19.6 18.4842109302784 1.11578906972161 25 20.9 19.3321860299671 1.56781397003295 26 21 20.8000627325591 0.199937267440922 27 19.9 21.2568249130978 -1.35682491309780 28 19.6 19.6032917722089 -0.00329177220886537 29 20.9 19.2773558427754 1.6226441572246 30 21.7 21.0550634427402 0.644936557259845 31 22.9 22.2245533387223 0.675446661277677 32 21.5 22.7532089299502 -1.25320892995017 33 21.3 21.8228762377230 -0.522876237723018 34 23.5 21.158847713339 2.34115228666101 35 21.6 23.6015163682619 -2.00151636826194 36 24.5 21.8949714881926 2.6050285118074 37 22.2 23.1482666099516 -0.94826660995159 38 23.5 23.2359194878293 0.264080512170718 39 20.9 22.2026859972483 -1.3026859972483 40 20.7 21.4651643555195 -0.765164355519465 41 18.1 19.7851384662620 -1.68513846626202 42 17.1 18.7740155782133 -1.67401557821328 43 14.8 16.7428288289092 -1.94282882890921 44 13.8 15.1418467955614 -1.34184679556143 45 15.2 13.7458584562475 1.45414154375251 46 16 16.032029035693 -0.0320290356930054 47 17.6 17.1353783680852 0.46462163191484 48 15 17.5489166373005 -2.54891663730046 49 15 15.6754917942129 -0.675491794212917 50 16.3 14.3466930809153 1.95330691908474 51 19.4 16.9074902087468 2.49250979125315 52 21.3 19.8164973132801 1.48350268671991 53 20.5 22.2699460944688 -1.76994609446879 54 21.1 21.1323387820086 -0.0323387820086480 55 21.6 20.9260310431448 0.67396895685518 56 22.6 21.9136117585834 0.68638824141658 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.19311366928071 0.38622733856142 0.80688633071929 22 0.478871219971892 0.957742439943783 0.521128780028108 23 0.682137564780425 0.63572487043915 0.317862435219575 24 0.588520673848601 0.822958652302798 0.411479326151399 25 0.495137437679358 0.990274875358716 0.504862562320642 26 0.368301597361017 0.736603194722035 0.631698402638983 27 0.35292727849534 0.70585455699068 0.64707272150466 28 0.24059073375981 0.48118146751962 0.75940926624019 29 0.230282844508911 0.460565689017821 0.76971715549109 30 0.172792839693763 0.345585679387527 0.827207160306237 31 0.136846917334994 0.273693834669987 0.863153082665006 32 0.119457520440973 0.238915040881947 0.880542479559027 33 0.0659959104559046 0.131991820911809 0.934004089544095 34 0.084928085005692 0.169856170011384 0.915071914994308 35 0.0604199213477978 0.120839842695596 0.939580078652202 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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