*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 04:55:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227787029r3go6mrveg6p231.htm/, Retrieved Thu, 27 Nov 2008 11:57:09 +0000

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/2008/Nov/27/t1227787029r3go6mrveg6p231.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1 1 16 1 29 1 56 1 51 1 50 1 37 1 20 1 47 1 49 1 39 1 30 1 0 1 14 1 36 1 72 1 41 1 43 1 44 1 18 1 56 1 57 1 49 1 31 1 17 1 22 1 49 1 65 1 55 1 48 1 50 1 15 1 60 1 56 1 40 1 31 1 20 0 27 0 14 0 67 0 64 0 46 0 60 0 22 0 65 0 58 0 42 0 32 0 25 0 20 0 27 0 72 0 68 0 51 0 53 0 18 0 54 0 67 0 40 0 45 0 25 1 36 1 50 1 64 1 50 1 43 1 51 1 12 1 58 1 50 1 50 1 31 1

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation S[t] = + 44.0416666666667 -4.16666666666667D[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) 44.0416666666667 3.616612 12.1776 0 0 D -4.16666666666667 4.429428 -0.9407 0.350105 0.175052 Multiple Linear Regression - Regression Statistics Multiple R 0.111728600665064 R-squared 0.0124832802065734 Adjusted R-squared -0.00162410150476111 F-TEST (value) 0.884875766602643 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.350104649437324 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 17.7177104024409 Sum Squared Residuals 21974.2083333333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 39.8749999999999 -38.8749999999999 2 16 39.875 -23.875 3 29 39.875 -10.875 4 56 39.875 16.125 5 51 39.875 11.125 6 50 39.875 10.125 7 37 39.875 -2.875 8 20 39.875 -19.875 9 47 39.875 7.125 10 49 39.875 9.125 11 39 39.875 -0.875000000000002 12 30 39.875 -9.875 13 0 39.875 -39.875 14 14 39.875 -25.875 15 36 39.875 -3.875 16 72 39.875 32.125 17 41 39.875 1.12500000000000 18 43 39.875 3.125 19 44 39.875 4.125 20 18 39.875 -21.875 21 56 39.875 16.125 22 57 39.875 17.125 23 49 39.875 9.125 24 31 39.875 -8.875 25 17 39.875 -22.875 26 22 39.875 -17.875 27 49 39.875 9.125 28 65 39.875 25.125 29 55 39.875 15.125 30 48 39.875 8.125 31 50 39.875 10.125 32 15 39.875 -24.875 33 60 39.875 20.125 34 56 39.875 16.125 35 40 39.875 0.124999999999998 36 31 39.875 -8.875 37 20 44.0416666666667 -24.0416666666667 38 27 44.0416666666667 -17.0416666666667 39 14 44.0416666666667 -30.0416666666667 40 67 44.0416666666667 22.9583333333333 41 64 44.0416666666667 19.9583333333333 42 46 44.0416666666667 1.95833333333333 43 60 44.0416666666667 15.9583333333333 44 22 44.0416666666667 -22.0416666666667 45 65 44.0416666666667 20.9583333333333 46 58 44.0416666666667 13.9583333333333 47 42 44.0416666666667 -2.04166666666667 48 32 44.0416666666667 -12.0416666666667 49 25 44.0416666666667 -19.0416666666667 50 20 44.0416666666667 -24.0416666666667 51 27 44.0416666666667 -17.0416666666667 52 72 44.0416666666667 27.9583333333333 53 68 44.0416666666667 23.9583333333333 54 51 44.0416666666667 6.95833333333333 55 53 44.0416666666667 8.95833333333333 56 18 44.0416666666667 -26.0416666666667 57 54 44.0416666666667 9.95833333333333 58 67 44.0416666666667 22.9583333333333 59 40 44.0416666666667 -4.04166666666667 60 45 44.0416666666667 0.95833333333333 61 25 39.875 -14.875 62 36 39.875 -3.875 63 50 39.875 10.125 64 64 39.875 24.125 65 50 39.875 10.125 66 43 39.875 3.125 67 51 39.875 11.125 68 12 39.875 -27.875 69 58 39.875 18.125 70 50 39.875 10.125 71 50 39.875 10.125 72 31 39.875 -8.875 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.925282215840936 0.149435568318129 0.0747177841590645 6 0.902094799593818 0.195810400812364 0.0979052004061819 7 0.83250975650503 0.334980486989939 0.167490243494969 8 0.792826945799882 0.414346108400236 0.207173054200118 9 0.743248018141036 0.513503963717928 0.256751981858964 10 0.696397616981632 0.607204766036735 0.303602383018368 11 0.601599085721111 0.796801828557777 0.398400914278889 12 0.514916492150119 0.970167015699763 0.485083507849881 13 0.755496806165336 0.489006387669328 0.244503193834664 14 0.77365338098491 0.452693238030178 0.226346619015089 15 0.708348730328268 0.583302539343464 0.291651269671732 16 0.879010651174276 0.241978697651448 0.120989348825724 17 0.837148467071914 0.325703065856171 0.162851532928086 18 0.790457815950975 0.419084368098049 0.209542184049025 19 0.738970347276915 0.52205930544617 0.261029652723085 20 0.750150247324771 0.499699505350459 0.249849752675229 21 0.752268615967889 0.495462768064223 0.247731384032112 22 0.755496340469216 0.489007319061568 0.244503659530784 23 0.714236228649146 0.571527542701709 0.285763771350854 24 0.662727058896191 0.674545882207618 0.337272941103809 25 0.696080678231661 0.607838643536677 0.303919321768339 26 0.693754790027183 0.612490419945633 0.306245209972817 27 0.651447768679052 0.697104462641897 0.348552231320948 28 0.715276352059343 0.569447295881314 0.284723647940657 29 0.697551774403176 0.604896451193649 0.302448225596824 30 0.647131130038028 0.705737739923944 0.352868869961972 31 0.600882456742721 0.798235086514558 0.399117543257279 32 0.667282259500993 0.665435480998013 0.332717740499007 33 0.677175205222875 0.64564958955425 0.322824794777125 34 0.660132962850824 0.679734074298353 0.339867037149176 35 0.595161253613487 0.809677492773025 0.404838746386513 36 0.548184863024844 0.903630273950311 0.451815136975156 37 0.546107654123068 0.907784691753864 0.453892345876932 38 0.519261258726988 0.961477482546024 0.480738741273012 39 0.588870045637428 0.822259908725144 0.411129954362572 40 0.717338792251678 0.565322415496645 0.282661207748322 41 0.754058498739881 0.491883002520237 0.245941501260119 42 0.698492245279831 0.603015509440338 0.301507754720169 43 0.689063936408978 0.621872127182044 0.310936063591022 44 0.722146003591551 0.555707992816898 0.277853996408449 45 0.74589211835286 0.508215763294281 0.254107881647141 46 0.722878003999171 0.554243992001657 0.277121996000828 47 0.658700109252108 0.682599781495783 0.341299890747892 48 0.621716373628797 0.756567252742405 0.378283626371203 49 0.639906402731886 0.720187194536228 0.360093597268114 50 0.72642266817545 0.5471546636491 0.27357733182455 51 0.763345468532149 0.473309062935702 0.236654531467851 52 0.818410460470793 0.363179079058414 0.181589539529207 53 0.84657600077276 0.306847998454481 0.153423999227240 54 0.79684640891237 0.40630718217526 0.20315359108763 55 0.745397213085803 0.509205573828393 0.254602786914197 56 0.866756289631792 0.266487420736417 0.133243710368209 57 0.815859399051173 0.368281201897654 0.184140600948827 58 0.847316282470228 0.305367435059545 0.152683717529772 59 0.784859354677075 0.430281290645850 0.215140645322925 60 0.703188792905569 0.593622414188862 0.296811207094431 61 0.721789546683628 0.556420906632745 0.278210453316372 62 0.650668846806545 0.69866230638691 0.349331153193455 63 0.548604796075389 0.902790407849223 0.451395203924611 64 0.586398520238911 0.827202959522178 0.413601479761089 65 0.476357636153857 0.952715272307714 0.523642363846143 66 0.335842477015047 0.671684954030095 0.664157522984953 67 0.233159518934284 0.466319037868569 0.766840481065716 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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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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