Multiple Regression

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

Title produced by software: Multiple Regression

Date of computation: Fri, 10 Dec 2010 09:31:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/10/t1291973377molzwzwb4mbexv4.htm/, Retrieved Fri, 10 Dec 2010 10:29:48 +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/2010/Dec/10/t1291973377molzwzwb4mbexv4.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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101.82 107.34 93.63 99.85 101.76 101.68 107.34 93.63 99.91 102.37 101.68 107.34 93.63 99.87 102.38 102.45 107.34 96.13 99.86 102.86 102.45 107.34 96.13 100.10 102.87 102.45 107.34 96.13 100.10 102.92 102.45 107.34 96.13 100.12 102.95 102.45 107.34 96.13 99.95 103.02 102.45 112.60 96.13 99.94 104.08 102.52 112.60 96.13 100.18 104.16 102.52 112.60 96.13 100.31 104.24 102.85 112.60 96.13 100.65 104.33 102.85 112.61 96.13 100.65 104.73 102.85 112.61 96.13 100.69 104.86 103.25 112.61 96.13 101.26 105.03 103.25 112.61 98.73 101.26 105.62 103.25 112.61 98.73 101.38 105.63 103.25 112.61 98.73 101.38 105.63 104.45 112.61 98.73 101.38 105.94 104.45 112.61 98.73 101.44 106.61 104.45 118.65 98.73 101.40 107.69 104.80 118.65 98.73 101.40 107.78 104.80 118.65 98.73 100.58 107.93 105.29 118.65 98.73 100.58 108.48 105.29 114.29 98.73 100.58 108.14 105.29 114.29 98.73 100.59 108.48 105.29 114.29 98.73 100.81 108.48 106.04 114.29 101.67 100.75 108.89 105.94 114.29 101.67 100.75 108.93 105.94 114.29 etc...

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 17 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Cultuuruitgaven[t] = + 29.7574433780084 + 0.117381875008493Bioscoop[t] + 0.351226236672809Schouwburgabonnement[t] + 0.441727025825754Eendagsattracties[t] -0.186900472395651DVDhuren[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) 29.7574433780084 15.839775 1.8787 0.065797 0.032898 Bioscoop 0.117381875008493 0.043112 2.7227 0.008746 0.004373 Schouwburgabonnement 0.351226236672809 0.032757 10.7221 0 0 Eendagsattracties 0.441727025825754 0.048367 9.1328 0 0 DVDhuren -0.186900472395651 0.192568 -0.9706 0.336171 0.168085 Multiple Linear Regression - Regression Statistics Multiple R 0.993690183423486 R-squared 0.987420180632202 Adjusted R-squared 0.986470760302557 F-TEST (value) 1040.02426512321 F-TEST (DF numerator) 4 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.648444676422854 Sum Squared Residuals 22.2854664142004 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.76 102.106779395192 -0.346779395192457 2 102.37 102.079131904347 0.290868095652892 3 102.38 102.086607923243 0.293392076757049 4 102.86 103.283178536288 -0.423178536287826 5 102.87 103.238322422913 -0.368322422912866 6 102.92 103.238322422913 -0.318322422912869 7 102.95 103.234584413465 -0.284584413464953 8 103.02 103.266357493772 -0.246357493772220 9 104.08 105.115676503395 -1.03567650339515 10 104.16 105.079037121271 -0.919037121270786 11 104.24 105.054740059859 -0.814740059859354 12 104.33 105.029929917998 -0.69992991799763 13 104.73 105.033442180364 -0.303442180364355 14 104.86 105.025966161469 -0.165966161468535 15 105.03 104.966385642206 0.0636143577935919 16 105.62 106.114875909353 -0.494875909353369 17 105.63 106.092447852666 -0.462447852665901 18 105.63 106.092447852666 -0.462447852665901 19 105.94 106.233306102676 -0.293306102676091 20 106.61 106.222092074332 0.38790792566765 21 107.69 108.350974562732 -0.660974562731945 22 107.78 108.392058218985 -0.612058218984914 23 107.93 108.545316606349 -0.615316606349343 24 108.48 108.602833725104 -0.122833725103509 25 108.14 107.071487333210 1.06851266678994 26 108.48 107.069618328486 1.41038167151390 27 108.48 107.028500224559 1.45149977544094 28 108.89 108.426428115087 0.463571884913111 29 108.93 108.414689927586 0.515310072413968 30 109.21 108.375440828383 0.83455917161704 31 109.47 108.310025663044 1.15997433695552 32 109.8 108.288258344657 1.5117416553432 33 111.73 111.520461984212 0.209538015788098 34 111.85 111.553339987921 0.296660012078886 35 112.12 111.664852769179 0.455147230820828 36 112.15 111.691064361695 0.45893563830454 37 112.17 111.666767300284 0.50323269971597 38 112.67 111.718153245709 0.951846754290788 39 112.8 111.690118174850 1.10988182515013 40 113.44 114.459746626777 -1.01974662677734 41 113.53 114.452270607882 -0.922270607881512 42 114.53 114.505092451635 0.0249075483646654 43 114.51 114.432201267401 0.0777987325989709 44 115.05 114.869648081168 0.180351918831704 45 116.67 116.994545333775 -0.324545333775106 46 117.07 117.119240513553 -0.0492405135529845 47 116.92 117.122978523001 -0.202978523000891 48 117 117.147674243134 -0.147674243133571 49 117.02 117.161760068135 -0.141760068134595 50 117.35 117.193931807163 0.156068192836896 51 117.36 117.436036208487 -0.0760362084868141 52 117.82 118.465953115525 -0.645953115525012 53 117.88 118.483298317198 -0.603298317197728 54 118.24 118.541772701504 -0.301772701504318 55 118.5 118.545989343728 -0.0459893437284403 56 118.8 118.564679390968 0.235320609031993 57 119.76 119.923924926892 -0.163924926891772 58 120.09 119.905234879652 0.184765120347790 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.00184034838672653 0.00368069677345307 0.998159651613273 9 0.000187694040226690 0.000375388080453381 0.999812305959773 10 0.000372581020963318 0.000745162041926636 0.999627418979037 11 8.97282530085994e-05 0.000179456506017199 0.999910271746991 12 0.000669564714479248 0.00133912942895850 0.99933043528552 13 0.00140872422841514 0.00281744845683027 0.998591275771585 14 0.00124058724437448 0.00248117448874896 0.998759412755626 15 0.000417881197798112 0.000835762395596225 0.999582118802202 16 0.00021591653030957 0.00043183306061914 0.99978408346969 17 0.000100450269110630 0.000200900538221261 0.99989954973089 18 5.13896043247464e-05 0.000102779208649493 0.999948610395675 19 3.29743811754992e-05 6.59487623509984e-05 0.999967025618824 20 0.000209410436185487 0.000418820872370974 0.999790589563815 21 0.000244261959229843 0.000488523918459685 0.99975573804077 22 0.000419927170896413 0.000839854341792826 0.999580072829104 23 0.00540555550562405 0.0108111110112481 0.994594444494376 24 0.0364336350994665 0.072867270198933 0.963566364900533 25 0.170177259192661 0.340354518385322 0.829822740807339 26 0.34661128134239 0.69322256268478 0.65338871865761 27 0.399731459413797 0.799462918827595 0.600268540586203 28 0.394334477466819 0.788668954933637 0.605665522533181 29 0.410548387124336 0.821096774248672 0.589451612875664 30 0.396575172443671 0.793150344887342 0.603424827556329 31 0.376141823080641 0.752283646161282 0.623858176919359 32 0.396739792065361 0.793479584130722 0.603260207934639 33 0.396005612691516 0.792011225383032 0.603994387308484 34 0.380560637764111 0.761121275528223 0.619439362235889 35 0.543071386043575 0.913857227912851 0.456928613956425 36 0.607294301812052 0.785411396375896 0.392705698187948 37 0.633148381395999 0.733703237208003 0.366851618604001 38 0.562193503825147 0.875612992349707 0.437806496174853 39 0.499473746560957 0.998947493121914 0.500526253439043 40 0.75288781417514 0.494224371649719 0.247112185824859 41 0.9430628147221 0.113874370555802 0.0569371852779008 42 0.907556447360942 0.184887105278116 0.0924435526390578 43 0.858582444495312 0.282835111009377 0.141417555504688 44 0.990349141838077 0.0193017163238465 0.00965085816192326 45 0.99908588667435 0.00182822665129895 0.000914113325649476 46 0.998988969128568 0.00202206174286345 0.00101103087143172 47 0.99824148127637 0.00351703744725995 0.00175851872362997 48 0.99402662827275 0.011946743454498 0.005973371727249 49 0.978614513476346 0.0427709730473073 0.0213854865236536 50 0.937217346682039 0.125565306635923 0.0627826533179614 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.418604651162791 NOK 5% type I error level 22 0.511627906976744 NOK 10% type I error level 23 0.534883720930233 NOK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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