paper/7

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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: Wed, 30 Dec 2009 07:02:15 -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/30/t1262181793n6dk72wki35j56k.htm/, Retrieved Wed, 30 Dec 2009 15:03:25 +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/30/t1262181793n6dk72wki35j56k.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}, }

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Dataseries X:

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10519.20 1154.80 10414.90 1206.70 12476.80 1199.00 12384.60 1265.00 12266.70 1247.10 12919.90 1116.50 11497.30 1153.90 12142.00 1077.40 13919.40 1132.50 12656.80 1058.80 12034.10 1195.10 13199.70 1263.40 10881.30 1023.10 11301.20 1141.00 13643.90 1116.30 12517.00 1135.60 13981.10 1210.50 14275.70 1230.00 13425.00 1136.50 13565.70 1068.70 16216.30 1372.50 12970.00 1049.90 14079.90 1302.20 14235.00 1305.90 12213.40 1173.50 12581.00 1277.40 14130.40 1238.60 14210.80 1508.60 14378.50 1423.40 13142.80 1375.10 13714.70 1344.10 13621.90 1287.50 15379.80 1446.90 13306.30 1451.00 14391.20 1604.40 14909.90 1501.50 14025.40 1522.80 12951.20 1328.00 14344.30 1420.50 16093.40 1648.00 15413.60 1631.10 14705.70 1396.60 15972.80 1663.40 16241.40 1283.00 16626.40 1582.40 17136.20 1785.20 15622.90 1853.60 18003.90 1994.10 16136.10 2042.80 14423.70 1586.10 16789.40 1942.40 16782.20 1763.60 14133.80 1819.90 12607.00 1836.00 12004.50 1447.50 12175.40 1509.50 13268.00 1661.20 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation InvoerEU[t] = + 8364.55205053314 + 4.25910868244174InvoerAM[t] -1684.39974677317M1[t] -1600.38474977774M2[t] + 20.5273625242572M3[t] -202.968619017035M4[t] -575.369022465705M5[t] -758.070770420407M6[t] -787.57039184164M7[t] -118.799364083242M8[t] + 588.144644564955M9[t] -484.156862564042M10[t] -968.319152204772M11[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) 8364.55205053314 1129.858267 7.4032 0 0 InvoerAM 4.25910868244174 0.648476 6.5679 0 0 M1 -1684.39974677317 749.130925 -2.2485 0.029174 0.014587 M2 -1600.38474977774 790.955399 -2.0234 0.048624 0.024312 M3 20.5273625242572 783.865039 0.0262 0.979216 0.489608 M4 -202.968619017035 779.621155 -0.2603 0.795713 0.397857 M5 -575.369022465705 779.553346 -0.7381 0.464062 0.232031 M6 -758.070770420407 783.325933 -0.9678 0.338016 0.169008 M7 -787.57039184164 786.713665 -1.0011 0.321804 0.160902 M8 -118.799364083242 799.066207 -0.1487 0.882435 0.441217 M9 588.144644564955 780.563679 0.7535 0.454837 0.227419 M10 -484.156862564042 785.720098 -0.6162 0.540677 0.270339 M11 -968.319152204772 779.990381 -1.2415 0.220472 0.110236 Multiple Linear Regression - Regression Statistics Multiple R 0.764773460760515 R-squared 0.584878446283615 Adjusted R-squared 0.481098057854518 F-TEST (value) 5.63573190596804 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 6.45909708762993e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1231.29133474384 Sum Squared Residuals 72771760.8487324 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10519.2 11598.5710102437 -1079.37101024372 2 10414.9 11903.6337478578 -1488.73374785785 3 12476.8 13491.7507233050 -1014.95072330504 4 12384.6 13549.3559148049 -1164.7559148049 5 12266.7 13100.7174659405 -834.017465940526 6 12919.9 12361.7761240589 558.123875941065 7 11497.3 12491.5671673610 -994.267167361022 8 12142 12834.5163809126 -692.516380912629 9 13919.4 13776.1372779634 143.262722036637 10 12656.8 12389.9394609384 266.860539061589 11 12034.1 12486.2936847145 -452.19368471449 12 13199.7 13745.5099599300 -545.809959930032 13 10881.3 11037.6463967661 -156.34639676611 14 11301.2 11623.8103074214 -322.61030742142 15 13643.9 13139.5224352671 504.37756473289 16 12517 12998.2272512969 -481.227251296943 17 13981.1 12944.8340881632 1036.26591183684 18 14275.7 12845.1849595161 1430.51504048393 19 13425 12417.4586762865 1007.54132371346 20 13565.7 12797.4621353754 768.237864624616 21 16216.3 14798.3233617494 1417.97663825062 22 12970 12352.0333936647 617.96660633532 23 14079.9 12942.444224604 1137.455775396 24 14235 13926.5220789338 308.477921066193 25 12213.4 11678.2163426053 535.183657394653 26 12581 12204.7527317065 376.247268293526 27 14130.4 13660.4114271297 469.988572870266 28 14210.8 14586.8747898477 -376.074789847712 29 14378.5 13851.598326655 526.901673344994 30 13142.8 13463.1816293384 -320.381629338368 31 13714.7 13301.6496387614 413.050361238561 32 13621.9 13729.3551150936 -107.455115093637 33 15379.8 15115.2010477230 264.598952276953 34 13306.3 14060.3618861921 -754.061886192061 35 14391.2 14229.5468684379 161.653131562107 36 14909.9 14759.6037372194 150.296262780590 37 14025.4 13165.9230053822 859.476994617754 38 12951.2 12420.2636310380 530.936368961976 39 14344.3 14435.1432964659 -90.8432964658868 40 16093.4 15180.5945401801 912.80545981991 41 15413.6 14736.2151999982 677.384800001847 42 14705.7 13554.7524660109 1150.94753398914 43 15972.8 14661.5830410651 1311.21695893491 44 16241.4 13710.1891260226 2531.21087397735 45 16626.4 15692.3102741939 934.0897258061 46 17136.2 15483.7560078641 1652.44399213591 47 15622.9 15290.9167521024 331.983247897627 48 18003.9 16857.6406741902 1146.25932580979 49 16136.1 15380.6595202519 755.440479748052 50 14423.7 13519.5395819762 904.160418023764 51 16789.4 16657.9721178322 131.427882167772 52 16782.2 15672.9475038704 1109.25249612965 53 14133.8 15540.3349192432 -1406.53491924316 54 12607 15426.2048210758 -2819.20482107576 55 12004.5 13742.0414765259 -1737.54147652592 56 12175.4 14674.8772425957 -2499.47724259570 57 13268 16027.9280383703 -2759.92803837031 58 12299.3 14082.5092513408 -1783.20925134076 59 11800.6 12979.4984701412 -1178.89847014124 60 13873.3 14932.5235497265 -1059.22354972654 61 12315 13229.3837247506 -914.383724750628 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0486335984339357 0.0972671968678714 0.951366401566064 17 0.08549179595792 0.17098359191584 0.91450820404208 18 0.136320352114358 0.272640704228716 0.863679647885642 19 0.168295964981922 0.336591929963843 0.831704035018078 20 0.142005085249284 0.284010170498568 0.857994914750716 21 0.194037697206734 0.388075394413467 0.805962302793266 22 0.125660271838602 0.251320543677204 0.874339728161398 23 0.121575426482228 0.243150852964456 0.878424573517772 24 0.0818364569434377 0.163672913886875 0.918163543056562 25 0.0610996444340591 0.122199288868118 0.938900355565941 26 0.0450683416634895 0.090136683326979 0.95493165833651 27 0.0269004750948161 0.0538009501896323 0.973099524905184 28 0.0164703267371480 0.0329406534742959 0.983529673262852 29 0.00889727707681753 0.0177945541536351 0.991102722923182 30 0.00923115139797513 0.0184623027959503 0.990768848602025 31 0.00476725489038192 0.00953450978076384 0.995232745109618 32 0.00232407545790241 0.00464815091580483 0.997675924542098 33 0.00136450585447351 0.00272901170894701 0.998635494145526 34 0.000958698676184506 0.00191739735236901 0.999041301323816 35 0.000415587241278794 0.000831174482557587 0.999584412758721 36 0.000171642855824269 0.000343285711648538 0.999828357144176 37 0.000114694968796046 0.000229389937592091 0.999885305031204 38 5.85798574308129e-05 0.000117159714861626 0.99994142014257 39 2.02530337805781e-05 4.05060675611562e-05 0.99997974696622 40 1.30791739273208e-05 2.61583478546415e-05 0.999986920826073 41 6.77478604168934e-06 1.35495720833787e-05 0.999993225213958 42 3.98388975719368e-05 7.96777951438736e-05 0.999960161102428 43 3.31194979751479e-05 6.62389959502958e-05 0.999966880502025 44 0.0159538856167959 0.0319077712335918 0.984046114383204 45 0.332152560562777 0.664305121125554 0.667847439437223 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.433333333333333 NOK 5% type I error level 17 0.566666666666667 NOK 10% type I error level 20 0.666666666666667 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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