*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 07:44:36 -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/t1260888336zlu1m8mdqu6zvrv.htm/, Retrieved Tue, 15 Dec 2009 15:45:49 +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/t1260888336zlu1m8mdqu6zvrv.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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29 0 27 27 0 29 26 0 27 24 0 26 30 0 24 26 0 30 28 0 26 28 0 28 24 0 28 23 0 24 24 0 23 24 0 24 27 0 24 28 0 27 25 0 28 19 0 25 19 0 19 19 0 19 20 0 19 16 0 20 22 0 16 21 0 22 25 0 21 29 0 25 28 0 29 25 0 28 26 0 25 24 0 26 28 0 24 28 0 28 28 0 28 28 0 28 32 0 28 31 0 32 22 0 31 29 0 22 31 0 29 29 0 31 32 0 29 32 0 32 31 0 32 29 0 31 28 0 29 28 0 28 29 0 28 22 0 29 26 0 22 24 0 26 27 0 24 27 0 27 23 0 27 21 0 23 19 0 21 17 0 19 19 0 17 21 1 19 13 1 21 8 1 13 5 1 8 10 1 5 6 1 10 6 1 6 8 1 6 11 1 8 12 1 11 13 1 12 19 1 13 19 1 19 18 1 19 20 1 18

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] = + 6.75972454369191 -3.3267423757629X[t] + 0.731410997239706Y1[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) 6.75972454369191 2.280058 2.9647 0.004193 0.002097 X -3.3267423757629 1.462101 -2.2753 0.026091 0.013046 Y1 0.731410997239706 0.087178 8.3898 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.89694983314468 R-squared 0.804519003178269 Adjusted R-squared 0.798683749541799 F-TEST (value) 137.872156601751 F-TEST (DF numerator) 2 F-TEST (DF denominator) 67 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.10564792842612 Sum Squared Residuals 646.21828670761 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 29 26.507821469164 2.49217853083602 2 27 27.9706434636434 -0.970643463643395 3 26 26.507821469164 -0.507821469163974 4 24 25.7764104719243 -1.77641047192428 5 30 24.3135884774449 5.68641152255513 6 26 28.7020544608831 -2.7020544608831 7 28 25.7764104719243 2.22358952807572 8 28 27.2392324664037 0.76076753359631 9 24 27.2392324664037 -3.23923246640369 10 23 24.3135884774449 -1.31358847744487 11 24 23.5821774802052 0.41782251979484 12 24 24.3135884774449 -0.313588477444866 13 27 24.3135884774449 2.68641152255513 14 28 26.507821469164 1.49217853083602 15 25 27.2392324664037 -2.23923246640369 16 19 25.0449994746846 -6.04499947468457 17 19 20.6565334912463 -1.65653349124634 18 19 20.6565334912463 -1.65653349124634 19 20 20.6565334912463 -0.656533491246336 20 16 21.3879444884860 -5.38794448848604 21 22 18.4623004995272 3.53769950047278 22 21 22.8507664829655 -1.85076648296545 23 25 22.1193554857257 2.88064451427425 24 29 25.0449994746846 3.95500052531543 25 28 27.9706434636434 0.0293565363566031 26 25 27.2392324664037 -2.23923246640369 27 26 25.0449994746846 0.955000525315428 28 24 25.7764104719243 -1.77641047192428 29 28 24.3135884774449 3.68641152255513 30 28 27.2392324664037 0.76076753359631 31 28 27.2392324664037 0.76076753359631 32 28 27.2392324664037 0.76076753359631 33 32 27.2392324664037 4.76076753359631 34 31 30.1648764553625 0.835123544637484 35 22 29.4334654581228 -7.43346545812281 36 29 22.8507664829655 6.14923351703455 37 31 27.9706434636434 3.0293565363566 38 29 29.4334654581228 -0.433465458122809 39 32 27.9706434636434 4.0293565363566 40 32 30.1648764553625 1.83512354463748 41 31 30.1648764553625 0.835123544637484 42 29 29.4334654581228 -0.433465458122809 43 28 27.9706434636434 0.0293565363566031 44 28 27.2392324664037 0.76076753359631 45 29 27.2392324664037 1.76076753359631 46 22 27.9706434636434 -5.9706434636434 47 26 22.8507664829655 3.14923351703455 48 24 25.7764104719243 -1.77641047192428 49 27 24.3135884774449 2.68641152255513 50 27 26.507821469164 0.492178530836015 51 23 26.507821469164 -3.50782146916398 52 21 23.5821774802052 -2.58217748020516 53 19 22.1193554857257 -3.11935548572575 54 17 20.6565334912463 -3.65653349124634 55 19 19.1937114967669 -0.193711496766923 56 21 17.3297911154834 3.67020888451657 57 13 18.7926131099628 -5.79261310996285 58 8 12.9413251320452 -4.9413251320452 59 5 9.28427014584667 -4.28427014584666 60 10 7.09003715412755 2.90996284587245 61 6 10.7470921403261 -4.74709214032608 62 6 7.82144815136725 -1.82144815136725 63 8 7.82144815136725 0.178551848632747 64 11 9.28427014584667 1.71572985415333 65 12 11.4785031375658 0.521496862434216 66 13 12.2099141348055 0.79008586519451 67 19 12.9413251320452 6.0586748679548 68 19 17.3297911154834 1.67020888451657 69 18 17.3297911154834 0.670208884516567 70 20 16.5983801182437 3.40161988175627 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.443326081715525 0.88665216343105 0.556673918284475 7 0.282828177235815 0.565656354471629 0.717171822764185 8 0.182280158601985 0.364560317203969 0.817719841398015 9 0.187982459632941 0.375964919265881 0.81201754036706 10 0.314627267087729 0.629254534175458 0.68537273291227 11 0.258682765390492 0.517365530780984 0.741317234609508 12 0.19823766710833 0.39647533421666 0.80176233289167 13 0.149047230076197 0.298094460152394 0.850952769923803 14 0.111602178797097 0.223204357594194 0.888397821202903 15 0.0833968373361858 0.166793674672372 0.916603162663814 16 0.339958766256321 0.679917532512642 0.660041233743679 17 0.338994113307793 0.677988226615586 0.661005886692207 18 0.291736814683589 0.583473629367179 0.70826318531641 19 0.224917254006786 0.449834508013573 0.775082745993213 20 0.340236095167270 0.680472190334539 0.65976390483273 21 0.381138421446013 0.762276842892025 0.618861578553987 22 0.328664795810021 0.657329591620042 0.671335204189979 23 0.321508124106606 0.643016248213212 0.678491875893394 24 0.374007561219149 0.748015122438298 0.625992438780851 25 0.305189952239640 0.610379904479281 0.69481004776036 26 0.266809466913708 0.533618933827416 0.733190533086292 27 0.21543943766549 0.43087887533098 0.78456056233451 28 0.177776803171012 0.355553606342024 0.822223196828988 29 0.199707503530211 0.399415007060421 0.80029249646979 30 0.156816931316029 0.313633862632058 0.843183068683971 31 0.120288843029384 0.240577686058768 0.879711156970616 32 0.0900973090320702 0.180194618064140 0.90990269096793 33 0.138201728473799 0.276403456947597 0.861798271526201 34 0.104738640710238 0.209477281420475 0.895261359289762 35 0.316824408115116 0.633648816230231 0.683175591884884 36 0.503183324136944 0.993633351726112 0.496816675863056 37 0.504909776736042 0.990180446527916 0.495090223263958 38 0.434503871141082 0.869007742282164 0.565496128858918 39 0.489651595524234 0.979303191048469 0.510348404475766 40 0.449313623506426 0.898627247012852 0.550686376493574 41 0.388440462049491 0.776880924098982 0.611559537950509 42 0.321476126815846 0.642952253631692 0.678523873184154 43 0.261288266383298 0.522576532766595 0.738711733616702 44 0.214946798661964 0.429893597323927 0.785053201338036 45 0.19508133078218 0.39016266156436 0.80491866921782 46 0.300378155442173 0.600756310884345 0.699621844557827 47 0.32991131914784 0.65982263829568 0.67008868085216 48 0.273116029901586 0.546232059803172 0.726883970098414 49 0.299763371668734 0.599526743337468 0.700236628331266 50 0.265555074095564 0.531110148191129 0.734444925904436 51 0.232667316142154 0.465334632284309 0.767332683857846 52 0.189531642205322 0.379063284410644 0.810468357794678 53 0.158709656909888 0.317419313819777 0.841290343090112 54 0.148768257492390 0.297536514984779 0.85123174250761 55 0.104001121295977 0.208002242591955 0.895998878704023 56 0.0976178989887545 0.195235797977509 0.902382101011245 57 0.246982173955989 0.493964347911979 0.753017826044011 58 0.388350381246865 0.77670076249373 0.611649618753135 59 0.472330867026867 0.944661734053733 0.527669132973133 60 0.501182571769701 0.997634856460598 0.498817428230299 61 0.758908765198084 0.482182469603832 0.241091234801916 62 0.739701971658651 0.520596056682699 0.260298028341349 63 0.6363025743706 0.7273948512588 0.3636974256294 64 0.474955773292856 0.949911546585713 0.525044226707144 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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