*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 07:43:01 -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/t1258728291so34pda1a7drc1w.htm/, Retrieved Fri, 20 Nov 2009 15:45:03 +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/t1258728291so34pda1a7drc1w.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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115.6 37.2 111.9 37.2 107 34.7 107.1 32.5 100.6 33.5 99.2 31.5 108.4 31.2 103 27 99.8 26.7 115 26.5 90.8 26 95.9 27.2 114.4 30.5 108.2 33.7 112.6 34.2 109.1 36.7 105 36.2 105 38.5 118.5 40 103.7 42.5 112.5 43.5 116.6 43.3 96.6 45.5 101.9 44.3 116.5 43 119.3 43.5 115.4 41.5 108.5 42.5 111.5 41.3 108.8 39.5 121.8 38.5 109.6 41 112.2 44.5 119.6 46 104.1 44 105.3 41.5 115 41.3 124.1 38 116.8 38 107.5 36.2 115.6 38.7 116.2 38.7 116.3 39.2 119 35.7 111.9 36.5 118.6 36.7 106.9 34.7 103.2 35 118.6 28.2 118.7 23.7 102.8 15 100.6 8.7 94.9 11 94.5 7.5 102.9 5.7 95.3 9.3 92.5 10.2 102.7 15.7 91.5 18.1 89.5 20.8

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 Ipzb[t] = + 75.7409869117733 + 0.549150534516807Cvn[t] + 17.0989534888664M1[t] + 17.8337099537553M2[t] + 13.5730053380130M3[t] + 9.82430309154084M4[t] + 8.19845267982208M5[t] + 7.83205624092391M6[t] + 16.6573223851026M7[t] + 8.96292831547462M8[t] + 7.83938371132981M9[t] + 15.6769920109720M10[t] -0.989537973133346M11[t] + 0.135546973414980t + 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) 75.7409869117733 3.208801 23.6041 0 0 Cvn 0.549150534516807 0.054863 10.0095 0 0 M1 17.0989534888664 2.562351 6.6731 0 0 M2 17.8337099537553 2.559247 6.9683 0 0 M3 13.5730053380130 2.562525 5.2967 3e-06 2e-06 M4 9.82430309154084 2.564728 3.8305 0.000386 0.000193 M5 8.19845267982208 2.556536 3.2069 0.002443 0.001222 M6 7.83205624092391 2.55751 3.0624 0.003662 0.001831 M7 16.6573223851026 2.555156 6.5191 0 0 M8 8.96292831547462 2.551279 3.5131 0.001005 0.000503 M9 7.83938371132981 2.544659 3.0807 0.003481 0.00174 M10 15.6769920109720 2.540776 6.1702 0 0 M11 -0.989537973133346 2.540027 -0.3896 0.698647 0.349323 t 0.135546973414980 0.034394 3.941 0.000274 0.000137 Multiple Linear Regression - Regression Statistics Multiple R 0.913511293399156 R-squared 0.8345028831678 Adjusted R-squared 0.787731958845656 F-TEST (value) 17.8423431921081 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 9.15933995315754e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.01570337139246 Sum Squared Residuals 741.790184082586 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 115.6 113.40388725808 2.19611274191999 2 111.9 114.274190696384 -2.37419069638375 3 107 108.776156717764 -1.77615671776442 4 107.1 103.954870268770 3.14512973122969 5 100.6 103.013717364983 -2.41371736498335 6 99.2 101.684566830467 -2.48456683046652 7 108.4 110.480634787705 -2.08063478770517 8 103 100.615355446522 2.38464455347843 9 99.8 99.4626126554367 0.337387344563305 10 115 107.325937821590 7.67406217840954 11 90.8 90.5203795436417 0.279620456358269 12 95.9 92.3044451316102 3.59555486838979 13 114.4 111.351142357797 3.04885764220289 14 108.2 113.978727506555 -5.77872750655469 15 112.6 110.128145131486 2.47185486851421 16 109.1 107.887866194721 1.21213380527934 17 105 106.122987489158 -1.12298748915847 18 105 107.155184253064 -2.15518425306394 19 118.5 116.939723172433 1.56027682756716 20 103.7 110.753752412512 -7.05375241251183 21 112.5 110.314905316299 2.18509468370119 22 116.6 118.178230482453 -1.57823048245260 23 96.6 102.855378647699 -6.25537864769924 24 101.9 103.321482952827 -1.42148295282738 25 116.5 119.842087720237 -3.34208772023697 26 119.3 120.986966425799 -1.68696642579916 27 115.4 115.763507714438 -0.363507714438231 28 108.5 112.699502975898 -4.1995029758979 29 111.5 110.550218896174 0.949781103826055 30 108.8 109.330898468561 -0.53089846856051 31 121.8 117.742561051637 4.0574389483626 32 109.6 111.556590291716 -1.95659029171639 33 112.2 112.490619531795 -0.290619531795379 34 119.6 121.287500606628 -1.68750060662774 35 104.1 103.658216526904 0.441783473096213 36 105.3 103.410425137160 1.88957486283991 37 115 120.535095492538 -5.53509549253816 38 124.1 119.593202166936 4.50679783306351 39 116.8 115.468044524609 1.33195547539082 40 107.5 110.866418289422 -3.36641828942178 41 115.6 110.74899118741 4.85100881258998 42 116.2 110.518141721927 5.68185827807318 43 116.3 119.753530106779 -3.45353010677893 44 119 110.272656139757 8.72734386024292 45 111.9 109.723978936641 2.17602106335931 46 118.6 117.806964316601 0.793035683398797 47 106.9 100.177680236877 6.72231976312276 48 103.2 101.467510343781 1.73248965621940 49 118.6 114.967787171348 3.63221282865225 50 118.7 113.366913204326 5.3330867956741 51 102.8 104.464145911702 -1.66414591170238 52 100.6 97.3913422711893 3.20865772881065 53 94.9 97.1640850622742 -2.26408506227422 54 94.5 95.0112087259822 -0.51120872598221 55 102.9 102.983550881446 -0.083550881445649 56 95.3 97.4016457094931 -2.10164570949313 57 92.5 96.9078835598284 -4.40788355982843 58 102.7 107.901366772728 -5.20136677272801 59 91.5 92.688345044878 -1.18834504487801 60 89.5 95.2961364346217 -5.79613643462172 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.243481460600032 0.486962921200063 0.756518539399968 18 0.116357959017887 0.232715918035775 0.883642040982113 19 0.0748016405583889 0.149603281116778 0.925198359441611 20 0.277043656498803 0.554087312997606 0.722956343501197 21 0.279811458367422 0.559622916734845 0.720188541632578 22 0.32786340031502 0.65572680063004 0.67213659968498 23 0.267121953793194 0.534243907586387 0.732878046206806 24 0.185609030371583 0.371218060743165 0.814390969628417 25 0.152420894022175 0.304841788044351 0.847579105977825 26 0.166807953825635 0.333615907651271 0.833192046174365 27 0.108614912488365 0.217229824976729 0.891385087511635 28 0.117338175585636 0.234676351171273 0.882661824414364 29 0.100365501555851 0.200731003111702 0.89963449844415 30 0.0759266883270901 0.151853376654180 0.92407331167291 31 0.0770287051691976 0.154057410338395 0.922971294830802 32 0.0686389314928278 0.137277862985656 0.931361068507172 33 0.0411356390566211 0.0822712781132423 0.958864360943379 34 0.0269397144377801 0.0538794288755603 0.97306028556222 35 0.0297308989843244 0.0594617979686489 0.970269101015676 36 0.0162385098269018 0.0324770196538036 0.983761490173098 37 0.132215763844406 0.264431527688812 0.867784236155594 38 0.234651994669569 0.469303989339139 0.76534800533043 39 0.1663912638137 0.3327825276274 0.8336087361863 40 0.608131288665232 0.783737422669535 0.391868711334768 41 0.528509493212394 0.942981013575212 0.471490506787606 42 0.482653854624642 0.965307709249283 0.517346145375358 43 0.897426716618084 0.205146566763832 0.102573283381916 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 1 0.0370370370370370 OK 10% type I error level 4 0.148148148148148 NOK

Charts produced by software:

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Parameters (Session):

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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