*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: Sun, 13 Dec 2009 06:53:10 -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/13/t1260712643ibc2hmbizrr4h3c.htm/, Retrieved Sun, 13 Dec 2009 14:57:46 +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/13/t1260712643ibc2hmbizrr4h3c.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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99.9 98.8 98.6 100.5 107.2 110.4 95.7 96.4 93.7 101.9 106.7 106.2 86.7 81 95.3 94.7 99.3 101 101.8 109.4 96 102.3 91.7 90.7 95.3 96.2 96.6 96.1 107.2 106 108 103.1 98.4 102 103.1 104.7 81.1 86 96.6 92.1 103.7 106.9 106.6 112.6 97.6 101.7 87.6 92 99.4 97.4 98.5 97 105.2 105.4 104.6 102.7 97.5 98.1 108.9 104.5 86.8 87.4 88.9 89.9 110.3 109.8 114.8 111.7 94.6 98.6 92 96.9 93.8 95.1 93.8 97 107.6 112.7 101 102.9 95.4 97.4 96.5 111.4 89.2 87.4 87.1 96.8 110.5 114.1 110.8 110.3 104.2 103.9 88.9 101.6 89.8 94.6 90 95.9 93.9 104.7 91.3 102.8 87.8 98.1 99.7 113.9 73.5 80.9 79.2 95.7 96.9 113.2 95.2 105.9 95.6 108.8 89.7 102.3

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 TotProd[t] = + 68.9998726894388 + 0.272276741690668ProdMetal[t] -0.843105051703042M1[t] -0.0138936993450399M2[t] + 8.0629457216336M3[t] + 2.83037297108659M4[t] + 2.17532426340796M5[t] + 8.43384670689379M6[t] -9.94021868678311M7[t] -2.35189545873824M8[t] + 8.71128351209637M9[t] + 9.1395056597435M10[t] + 4.37415861979585M11[t] + 0.088907391478745t + 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) 68.9998726894388 8.871394 7.7778 0 0 ProdMetal 0.272276741690668 0.092205 2.953 0.004944 0.002472 M1 -0.843105051703042 2.033966 -0.4145 0.680425 0.340213 M2 -0.0138936993450399 2.030811 -0.0068 0.994571 0.497285 M3 8.0629457216336 2.327675 3.4639 0.001163 0.000581 M4 2.83037297108659 2.158227 1.3114 0.19622 0.09811 M5 2.17532426340796 2.014348 1.0799 0.28581 0.142905 M6 8.43384670689379 2.282024 3.6958 0.000582 0.000291 M7 -9.94021868678311 2.088901 -4.7586 2e-05 1e-05 M8 -2.35189545873824 1.983136 -1.1859 0.241733 0.120866 M9 8.71128351209637 2.352284 3.7033 0.000569 0.000284 M10 9.1395056597435 2.446804 3.7353 0.000516 0.000258 M11 4.37415861979585 2.095697 2.0872 0.042438 0.021219 t 0.088907391478745 0.026525 3.3518 0.001613 0.000806 Multiple Linear Regression - Regression Statistics Multiple R 0.937242633290538 R-squared 0.878423753657381 Adjusted R-squared 0.844065249256206 F-TEST (value) 25.5664141663670 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.12812386152141 Sum Squared Residuals 450.117309078901 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.8 95.4461215241126 3.35387847588742 2 100.5 96.0102805037512 4.4897194962488 3 110.4 106.517607294748 3.88239270525169 4 96.4 98.2427594062374 -1.84275940623736 5 101.9 97.1320646066561 4.76793539334386 6 106.2 107.019092083599 -0.81909208359941 7 81 83.2883992475879 -2.28839924758789 8 94.7 93.3072098456512 1.39279015434875 9 101 105.548403174727 -4.54840317472728 10 109.4 106.746224568080 2.65377543192018 11 102.3 100.490579817805 1.80942018219495 12 90.7 95.034538600218 -4.33453860021807 13 96.2 95.2605372100802 0.93946278991982 14 96.1 96.5326157181148 -0.432615718114795 15 106 107.584495992493 -1.58449599249326 16 103.1 102.658652026778 0.441347973222465 17 102 99.4786539903472 2.52134600965277 18 104.7 107.105784511258 -2.40578451125794 19 86 82.8305381918651 3.16946180813492 20 92.1 94.728058307594 -2.62805830759406 21 106.9 107.813309535911 -0.913309535911158 22 112.6 109.12004162594 3.47995837406003 23 101.7 101.993111302255 -0.293111302255055 24 92 94.9850926570313 -2.98509265703126 25 97.4 97.4437605487569 -0.0437605487568535 26 97 98.116830225072 -1.11683022507200 27 105.4 108.106831206857 -2.70683120685685 28 102.7 102.799799802774 -0.0997998027741924 29 98.1 100.300493620571 -2.20049362057057 30 104.5 109.751878310809 -5.25187831080876 31 87.4 85.4494043172468 1.95059568275317 32 89.9 93.6984160943208 -3.79841609432085 33 109.8 110.677224728815 -0.87722472881452 34 111.7 112.419599605548 -0.719599605548383 35 98.6 102.243169774928 -3.643169774928 36 96.9 97.2499990182151 -0.349999018215143 37 95.1 96.985899493034 -1.88589949303406 38 97 97.9040182368708 -0.904018236870802 39 112.7 109.827184084659 2.8728159153406 40 102.9 102.886492230433 0.0135077695672743 41 97.4 100.795601160765 -3.39560116076510 42 111.4 107.442535411589 3.9574645884106 43 87.4 87.1697571950494 0.230242804950623 44 96.8 94.2752066570226 2.52479334297741 45 114.1 111.798568774898 2.3014312251024 46 110.3 112.397381336531 -2.09738133653066 47 103.9 105.923915192903 -2.02391519290335 48 101.6 97.472829816719 4.12717018328098 49 94.6 96.9636812240163 -2.36368122401633 50 95.9 97.9362553161912 -2.0362553161912 51 104.7 107.163881421242 -2.46388142124219 52 102.8 101.312296533778 1.48770346622181 53 98.1 99.793186621661 -1.69318662166097 54 113.9 109.380709682744 4.51929031725551 55 80.9 83.9619010482508 -3.06190104825082 56 95.7 93.1911090954112 2.50889090458875 57 113.2 109.162493785649 4.03750621435056 58 105.9 109.216752863901 -3.31675286390117 59 108.8 104.649223912109 4.15077608789145 60 102.3 98.7575399078165 3.5424600921835 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.157966862556138 0.315933725112277 0.842033137443862 18 0.126174460787153 0.252348921574307 0.873825539212847 19 0.630897981504623 0.738204036990754 0.369102018495377 20 0.545280184278947 0.909439631442106 0.454719815721053 21 0.540647147513094 0.918705704973811 0.459352852486906 22 0.600787709039201 0.798424581921598 0.399212290960799 23 0.543943750433120 0.91211249913376 0.45605624956688 24 0.479612826693043 0.959225653386087 0.520387173306956 25 0.421659004518302 0.843318009036603 0.578340995481698 26 0.354392604218404 0.708785208436808 0.645607395781596 27 0.280286169854181 0.560572339708363 0.719713830145819 28 0.225736145335122 0.451472290670244 0.774263854664878 29 0.247792537761854 0.495585075523709 0.752207462238146 30 0.477092483165208 0.954184966330415 0.522907516834792 31 0.644080174041965 0.71183965191607 0.355919825958035 32 0.685790349687403 0.628419300625193 0.314209650312597 33 0.67882380043482 0.64235239913036 0.32117619956518 34 0.682683854734029 0.634632290531942 0.317316145265971 35 0.607225033224068 0.785549933551864 0.392774966775932 36 0.67389312331339 0.652213753373219 0.326106876686610 37 0.571839423725043 0.856321152549914 0.428160576274957 38 0.486959338478045 0.97391867695609 0.513040661521955 39 0.70818286467156 0.58363427065688 0.29181713532844 40 0.611361172558048 0.777277654883904 0.388638827441952 41 0.509556546380737 0.980886907238525 0.490443453619263 42 0.52512394561262 0.94975210877476 0.47487605438738 43 0.505214681236331 0.989570637527338 0.494785318763669 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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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