*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: Mon, 07 Dec 2009 13:08:54 -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/07/t12602170496h2p9d2zbyhvemi.htm/, Retrieved Mon, 07 Dec 2009 21:17:43 +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/07/t12602170496h2p9d2zbyhvemi.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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111,5 0 0 108,1 0 0 124,5 0 0 106,3 0 0 111,1 0 0 121,3 0 0 116,5 0 0 117,4 0 0 123,6 0 0 98,4 0 0 107,2 0 0 118,9 0 0 111,9 0 0 115,2 0 0 124,4 0 0 104,6 0 0 117 0 0 126,2 0 0 117,5 0 0 122,2 0 0 124,1 0 0 105,8 0 0 107,5 0 0 125,6 0 0 112,1 0 0 120,1 0 0 130,6 0 0 109,8 0 0 122,1 0 0 129,5 0 0 132,1 0 0 133,3 0 0 128,4 0 0 114,7 0 1 114,1 0 1 136,9 0 1 123,4 0 1 134 0 1 137 0 1 127,8 0 1 140,1 0 1 140,4 0 1 157,8 0 1 151,8 0 1 141,1 0 1 138,8 1 0 141,1 1 0 139,5 1 0 150,7 1 0 144,4 1 0 146 1 0 143,6 1 0 143,1 1 0 156,4 1 0 164,8 1 0 145,1 1 0 153,4 1 0 133,2 1 0 131,4 1 0 145,9 1 0

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Omzet_Voedingssector[t] = + 112.043333333333 + 17.6541666666666Dummy_1_tijdenscrisis[t] + 10.3375000000000Dummy_2_voorcrisis[t] -4.18520833333336M1[t] -2.08374999999999M2[t] + 5.71770833333334M3[t] -8.70083333333333M4[t] -0.779375000000002M5[t] + 6.96208333333334M6[t] + 9.60354166666667M7[t] + 5.485M8[t] + 5.30645833333334M9[t] -14.5029166666667M10[t] -12.7614583333333M11[t] + 0.338541666666668t + 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) 112.043333333333 3.048852 36.7494 0 0 Dummy_1_tijdenscrisis 17.6541666666666 3.919616 4.5041 4.7e-05 2.3e-05 Dummy_2_voorcrisis 10.3375000000000 2.85194 3.6247 0.000733 0.000367 M1 -4.18520833333336 3.449751 -1.2132 0.231387 0.115693 M2 -2.08374999999999 3.440867 -0.6056 0.54783 0.273915 M3 5.71770833333334 3.434707 1.6647 0.102924 0.051462 M4 -8.70083333333333 3.431286 -2.5357 0.014764 0.007382 M5 -0.779375000000002 3.430612 -0.2272 0.821311 0.410655 M6 6.96208333333334 3.432686 2.0282 0.048487 0.024243 M7 9.60354166666667 3.437504 2.7938 0.007627 0.003813 M8 5.485 3.445054 1.5921 0.118355 0.059178 M9 5.30645833333334 3.455319 1.5357 0.131605 0.065803 M10 -14.5029166666667 3.418784 -4.2421 0.000109 5.4e-05 M11 -12.7614583333333 3.414643 -3.7373 0.000523 0.000261 t 0.338541666666668 0.097117 3.4859 0.001106 0.000553 Multiple Linear Regression - Regression Statistics Multiple R 0.95214497336165 R-squared 0.90658005029786 Adjusted R-squared 0.877516065946082 F-TEST (value) 31.1925591248959 F-TEST (DF numerator) 14 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.39684115427205 Sum Squared Residuals 1310.66525000000 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 111.5 108.196666666667 3.30333333333314 2 108.1 110.636666666667 -2.53666666666665 3 124.5 118.776666666667 5.72333333333332 4 106.3 104.696666666667 1.60333333333333 5 111.1 112.956666666667 -1.85666666666665 6 121.3 121.036666666667 0.263333333333348 7 116.5 124.016666666667 -7.51666666666665 8 117.4 120.236666666667 -2.83666666666665 9 123.6 120.396666666667 3.20333333333335 10 98.4 100.925833333333 -2.52583333333332 11 107.2 103.005833333333 4.19416666666669 12 118.9 116.105833333333 2.79416666666668 13 111.9 112.259166666667 -0.359166666666594 14 115.2 114.699166666667 0.500833333333344 15 124.4 122.839166666667 1.56083333333336 16 104.6 108.759166666667 -4.15916666666666 17 117 117.019166666667 -0.0191666666666566 18 126.2 125.099166666667 1.10083333333334 19 117.5 128.079166666667 -10.5791666666667 20 122.2 124.299166666667 -2.09916666666667 21 124.1 124.459166666667 -0.359166666666669 22 105.8 104.988333333333 0.811666666666662 23 107.5 107.068333333333 0.431666666666664 24 125.6 120.168333333333 5.43166666666666 25 112.1 116.321666666667 -4.22166666666663 26 120.1 118.761666666667 1.33833333333332 27 130.6 126.901666666667 3.69833333333332 28 109.8 112.821666666667 -3.02166666666667 29 122.1 121.081666666667 1.01833333333332 30 129.5 129.161666666667 0.338333333333322 31 132.1 132.141666666667 -0.0416666666666844 32 133.3 128.361666666667 4.93833333333333 33 128.4 128.521666666667 -0.121666666666674 34 114.7 119.388333333333 -4.68833333333334 35 114.1 121.468333333333 -7.36833333333334 36 136.9 134.568333333333 2.33166666666667 37 123.4 130.721666666667 -7.32166666666662 38 134 133.161666666667 0.838333333333324 39 137 141.301666666667 -4.30166666666667 40 127.8 127.221666666667 0.57833333333333 41 140.1 135.481666666667 4.61833333333333 42 140.4 143.561666666667 -3.16166666666667 43 157.8 146.541666666667 11.2583333333333 44 151.8 142.761666666667 9.03833333333333 45 141.1 142.921666666667 -1.82166666666668 46 138.8 130.7675 8.03250000000002 47 141.1 132.8475 8.2525 48 139.5 145.9475 -6.4475 49 150.7 142.100833333333 8.5991666666667 50 144.4 144.540833333333 -0.140833333333334 51 146 152.680833333333 -6.68083333333333 52 143.6 138.600833333333 4.99916666666667 53 143.1 146.860833333333 -3.76083333333334 54 156.4 154.940833333333 1.45916666666667 55 164.8 157.920833333333 6.87916666666667 56 145.1 154.140833333333 -9.04083333333335 57 153.4 154.300833333333 -0.90083333333333 58 133.2 134.83 -1.63000000000002 59 131.4 136.91 -5.51 60 145.9 150.01 -4.11000000000001 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.161867754703721 0.323735509407442 0.838132245296279 19 0.102943784468146 0.205887568936292 0.897056215531854 20 0.0529624868267692 0.105924973653538 0.94703751317323 21 0.0252099642436298 0.0504199284872595 0.97479003575637 22 0.0190893275364194 0.0381786550728388 0.98091067246358 23 0.00918457499499346 0.0183691499899869 0.990815425005007 24 0.00628687272378304 0.0125737454475661 0.993713127276217 25 0.00466435188450528 0.00932870376901056 0.995335648115495 26 0.00353249791723448 0.00706499583446895 0.996467502082766 27 0.00218611510276286 0.00437223020552572 0.997813884897237 28 0.0009453365107126 0.0018906730214252 0.999054663489287 29 0.000513549118486737 0.00102709823697347 0.999486450881513 30 0.000185634078964958 0.000371268157929916 0.999814365921035 31 0.00229957640212048 0.00459915280424096 0.99770042359788 32 0.00309323893106042 0.00618647786212084 0.99690676106894 33 0.00143782061342227 0.00287564122684454 0.998562179386578 34 0.00115614520511388 0.00231229041022777 0.998843854794886 35 0.00252054637664675 0.0050410927532935 0.997479453623353 36 0.00157119617376098 0.00314239234752197 0.99842880382624 37 0.00989064829706142 0.0197812965941228 0.990109351702939 38 0.0084627908885721 0.0169255817771442 0.991537209111428 39 0.00455112197640158 0.00910224395280315 0.995448878023598 40 0.00797034524733044 0.0159406904946609 0.99202965475267 41 0.0079872322356235 0.015974464471247 0.992012767764377 42 0.0103364556213564 0.0206729112427127 0.989663544378644 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.52 NOK 5% type I error level 21 0.84 NOK 10% type I error level 22 0.88 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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