multiple lin regr inv

*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: Thu, 18 Dec 2008 09:48:04 -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/Dec/18/t122961896992716xqe07ohjrs.htm/, Retrieved Thu, 18 Dec 2008 17:49:29 +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/2008/Dec/18/t122961896992716xqe07ohjrs.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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93.0 0 99.2 0 112.2 0 112.1 0 103.3 0 108.2 0 90.4 0 72.8 0 111.0 0 117.9 0 111.3 0 110.5 0 94.8 0 100.4 0 132.1 0 114.6 0 101.9 0 130.2 0 84.0 0 86.4 0 122.3 0 120.9 0 110.2 0 112.6 0 102.0 0 105.0 0 130.5 0 115.5 0 103.7 0 130.9 0 89.1 0 93.8 0 123.8 0 111.9 0 118.3 0 116.9 0 103.6 1 116.6 1 141.3 1 107.0 1 125.2 1 136.4 1 91.6 1 95.3 1 132.3 1 130.6 1 131.9 1 118.6 1 114.3 1 111.3 1 126.5 1 112.1 1 119.3 1 142.4 1 101.1 1 97.4 1 129.1 1 136.9 1 129.8 1 123.9 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation INV[t] = + 108.158333333333 + 11.6125INVA[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) 108.158333333333 2.407374 44.9279 0 0 INVA 11.6125 3.806392 3.0508 0.003439 0.001719 Multiple Linear Regression - Regression Statistics Multiple R 0.371861362192992 R-squared 0.138280872692028 Adjusted R-squared 0.123423646359132 F-TEST (value) 9.30731413748835 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00343868245796719 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 14.4442430265208 Sum Squared Residuals 12100.8970833333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 93 108.158333333333 -15.1583333333335 2 99.2 108.158333333333 -8.95833333333333 3 112.2 108.158333333333 4.04166666666667 4 112.1 108.158333333333 3.94166666666667 5 103.3 108.158333333333 -4.85833333333333 6 108.2 108.158333333333 0.0416666666666738 7 90.4 108.158333333333 -17.7583333333333 8 72.8 108.158333333333 -35.3583333333333 9 111 108.158333333333 2.84166666666667 10 117.9 108.158333333333 9.74166666666668 11 111.3 108.158333333333 3.14166666666667 12 110.5 108.158333333333 2.34166666666667 13 94.8 108.158333333333 -13.3583333333333 14 100.4 108.158333333333 -7.75833333333332 15 132.1 108.158333333333 23.9416666666667 16 114.6 108.158333333333 6.44166666666667 17 101.9 108.158333333333 -6.25833333333332 18 130.2 108.158333333333 22.0416666666667 19 84 108.158333333333 -24.1583333333333 20 86.4 108.158333333333 -21.7583333333333 21 122.3 108.158333333333 14.1416666666667 22 120.9 108.158333333333 12.7416666666667 23 110.2 108.158333333333 2.04166666666667 24 112.6 108.158333333333 4.44166666666666 25 102 108.158333333333 -6.15833333333333 26 105 108.158333333333 -3.15833333333333 27 130.5 108.158333333333 22.3416666666667 28 115.5 108.158333333333 7.34166666666667 29 103.7 108.158333333333 -4.45833333333333 30 130.9 108.158333333333 22.7416666666667 31 89.1 108.158333333333 -19.0583333333333 32 93.8 108.158333333333 -14.3583333333333 33 123.8 108.158333333333 15.6416666666667 34 111.9 108.158333333333 3.74166666666668 35 118.3 108.158333333333 10.1416666666667 36 116.9 108.158333333333 8.74166666666668 37 103.6 119.770833333333 -16.1708333333333 38 116.6 119.770833333333 -3.17083333333334 39 141.3 119.770833333333 21.5291666666667 40 107 119.770833333333 -12.7708333333333 41 125.2 119.770833333333 5.42916666666667 42 136.4 119.770833333333 16.6291666666667 43 91.6 119.770833333333 -28.1708333333333 44 95.3 119.770833333333 -24.4708333333333 45 132.3 119.770833333333 12.5291666666667 46 130.6 119.770833333333 10.8291666666667 47 131.9 119.770833333333 12.1291666666667 48 118.6 119.770833333333 -1.17083333333334 49 114.3 119.770833333333 -5.47083333333334 50 111.3 119.770833333333 -8.47083333333334 51 126.5 119.770833333333 6.72916666666667 52 112.1 119.770833333333 -7.67083333333334 53 119.3 119.770833333333 -0.470833333333337 54 142.4 119.770833333333 22.6291666666667 55 101.1 119.770833333333 -18.6708333333333 56 97.4 119.770833333333 -22.3708333333333 57 129.1 119.770833333333 9.32916666666666 58 136.9 119.770833333333 17.1291666666667 59 129.8 119.770833333333 10.0291666666667 60 123.9 119.770833333333 4.12916666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.259240803454809 0.518481606909618 0.740759196545191 6 0.139556334045409 0.279112668090818 0.860443665954591 7 0.166534483339487 0.333068966678974 0.833465516660513 8 0.589339199545173 0.821321600909654 0.410660800454827 9 0.533269569327597 0.933460861344807 0.466730430672403 10 0.552632851387857 0.894734297224285 0.447367148612143 11 0.47780402831564 0.95560805663128 0.52219597168436 12 0.396854862193488 0.793709724386977 0.603145137806511 13 0.348127599717959 0.696255199435918 0.651872400282041 14 0.272115781243762 0.544231562487524 0.727884218756238 15 0.506163331910396 0.987673336179208 0.493836668089604 16 0.44767175951817 0.89534351903634 0.55232824048183 17 0.372032549730205 0.74406509946041 0.627967450269795 18 0.503674761543509 0.992650476912983 0.496325238456492 19 0.626449361016073 0.747101277967855 0.373550638983928 20 0.705928689993786 0.588142620012427 0.294071310006214 21 0.708936139427034 0.582127721145932 0.291063860572966 22 0.694440477271503 0.611119045456994 0.305559522728497 23 0.625824336871588 0.748351326256823 0.374175663128411 24 0.558084969295496 0.883830061409009 0.441915030704504 25 0.499374083071038 0.998748166142076 0.500625916928962 26 0.431939633094853 0.863879266189707 0.568060366905147 27 0.520524057499879 0.958951885000243 0.479475942500121 28 0.459824202012206 0.919648404024413 0.540175797987794 29 0.396534490360228 0.793068980720457 0.603465509639772 30 0.486218279460753 0.972436558921505 0.513781720539247 31 0.552672169142631 0.894655661714739 0.447327830857369 32 0.592933909197344 0.814132181605312 0.407066090802656 33 0.569268168200538 0.861463663598923 0.430731831799462 34 0.499688725826711 0.999377451653421 0.500311274173289 35 0.439283712111418 0.878567424222835 0.560716287888583 36 0.374870136990288 0.749740273980575 0.625129863009712 37 0.354324748424443 0.708649496848886 0.645675251575557 38 0.29711057879702 0.59422115759404 0.70288942120298 39 0.395712385876387 0.791424771752773 0.604287614123613 40 0.372296434479084 0.744592868958167 0.627703565520916 41 0.308443510795928 0.616887021591855 0.691556489204072 42 0.323301420521368 0.646602841042737 0.676698579478632 43 0.535168928829379 0.929662142341242 0.464831071170621 44 0.703438614084712 0.593122771830577 0.296561385915288 45 0.678015081371455 0.643969837257089 0.321984918628545 46 0.63384638098733 0.73230723802534 0.36615361901267 47 0.600609848535796 0.798780302928409 0.399390151464204 48 0.502278626585432 0.995442746829136 0.497721373414568 49 0.416259045752845 0.832518091505689 0.583740954247155 50 0.354595023534753 0.709190047069506 0.645404976465247 51 0.267838904915756 0.535677809831511 0.732161095084245 52 0.207934980877158 0.415869961754316 0.792065019122842 53 0.132286226498221 0.264572452996442 0.867713773501779 54 0.181044683919838 0.362089367839676 0.818955316080162 55 0.229084614340205 0.45816922868041 0.770915385659795 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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