paper/8

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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 07:18:10 -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/t1262182734b6os87tpta79jzu.htm/, Retrieved Wed, 30 Dec 2009 15:19:06 +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/t1262182734b6os87tpta79jzu.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:

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User-defined keywords:

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] = + 7623.86000848206 + 5.09243448478566InvoerAM[t] -1664.04362482707M1[t] -1568.84464521667M2[t] + 3.7771978710695M3[t] -272.409013120862M4[t] -632.033570988034M5[t] -737.126725938879M6[t] -717.184166475482M7[t] + 52.7785744931061M8[t] + 612.799871961612M9[t] -379.126400499746M10[t] -926.162160895759M11[t] -14.6424953787492t + 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) 7623.86000848206 1363.540586 5.5912 1e-06 1e-06 InvoerAM 5.09243448478566 1.075473 4.7351 2e-05 1e-05 M1 -1664.04362482707 749.861072 -2.2191 0.031342 0.015671 M2 -1568.84464521667 792.082702 -1.9807 0.053499 0.02675 M3 3.7771978710695 784.512167 0.0048 0.996179 0.498089 M4 -272.409013120862 783.343574 -0.3478 0.729579 0.36479 M5 -632.033570988034 782.185802 -0.808 0.423141 0.211571 M6 -737.126725938879 784.079674 -0.9401 0.351964 0.175982 M7 -717.184166475482 790.49951 -0.9073 0.368901 0.18445 M8 52.7785744931061 818.802849 0.0645 0.948879 0.474439 M9 612.799871961612 781.431567 0.7842 0.436856 0.218428 M10 -379.126400499746 793.576109 -0.4777 0.635047 0.317523 M11 -926.162160895759 781.651002 -1.1849 0.242022 0.121011 t -14.6424953787492 15.070574 -0.9716 0.336226 0.168113 Multiple Linear Regression - Regression Statistics Multiple R 0.77009870414804 R-squared 0.593052014130491 Adjusted R-squared 0.480491932932542 F-TEST (value) 5.2687596510129 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.07896520391559e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1232.01025530412 Sum Squared Residuals 71338915.6512022 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10519.2 11825.9172313068 -1306.71723130677 2 10414.9 12170.7710652988 -1755.87106529876 3 12476.8 13689.5386674749 -1212.73866747490 4 12384.6 13734.8106371001 -1350.21063710007 5 12266.7 13269.3890065765 -1002.68900657648 6 12919.9 12484.5814125339 435.318587466116 7 11497.3 12680.3385263495 -1183.03852634952 8 12142 13046.0875338533 -904.087533853252 9 13919.4 13872.0594760547 47.3405239453025 10 12656.8 12490.1782866859 166.621713314112 11 12034.1 12622.5988511874 -588.498851187411 12 13199.7 13881.9317920153 -682.23179201528 13 10881.3 10979.5336651155 -98.2336651154673 14 11301.2 11660.4881751033 -359.288175103350 15 13643.9 13092.6843910381 551.215608961867 16 12517 12900.1396702238 -383.139670223814 17 13981.1 12907.2959598883 1073.80404011166 18 14275.7 12886.8627820121 1388.83721798793 19 13425 12416.0202217693 1008.97977823075 20 13565.7 12826.0734092906 739.626590709375 21 16216.3 14918.5338078583 1297.76619214173 22 12970 12269.1456752263 700.854324773695 23 14079.9 12992.2886399630 1087.61136003704 24 14235 13922.6503130737 312.349686926318 25 12213.4 11569.7258670822 643.67413291776 26 12581 12179.3862942831 401.613705716876 27 14130.4 13539.7791839824 590.620816017572 28 14210.8 14623.9077885039 -413.107788503876 29 14378.5 13815.7653171542 562.734682845783 30 13142.8 13450.0650812095 -307.265081209474 31 13714.7 13297.4996762658 417.200323734234 32 13621.9 13764.5881300167 -142.688130016738 33 15379.8 15121.7009889813 258.099011018671 34 13306.3 14136.0112025288 -829.711202528843 35 14391.2 14355.5123967202 35.6876032797997 36 14909.9 14743.0205537528 166.879446247234 37 14025.4 13172.8032880729 852.59671192712 38 12951.2 12261.3535346683 689.846465331713 39 14344.3 14290.3830722199 53.9169277800506 40 16093.4 15158.083211138 935.316788861994 41 15413.6 14697.7540150992 715.845984900793 42 14705.7 13383.8424780874 1321.85752191263 43 15972.8 14747.8040627128 1224.99593728716 44 16241.4 13565.9622302902 2675.43776970979 45 16626.4 15636.0159171248 990.384082875207 46 17136.2 15662.1928627992 1474.00713720078 47 15622.9 15448.8371257838 174.062874216204 48 18003.9 17075.8438364132 928.05616358681 49 16136.1 15645.1592756164 490.940724383567 50 14423.7 13400.0009306465 1023.69906935352 51 16789.4 16772.4146852846 16.9853147154062 52 16782.2 15571.0586930342 1211.14130696576 53 14133.8 15483.4957012818 -1349.69570128175 54 12607 15445.7482461572 -2838.74824615720 55 12004.5 13472.6375129026 -1468.13751290262 56 12175.4 14543.6886965492 -2368.28869654917 57 13268 15861.5898099809 -2593.58980998091 58 12299.3 13811.0719727597 -1511.77197275975 59 11800.6 12509.4629863456 -708.862986345628 60 13873.3 14598.3535047451 -725.053504745083 61 12315 12897.2606728062 -582.260672806206 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00527120595182335 0.0105424119036467 0.994728794048177 18 0.0170718440961165 0.0341436881922329 0.982928155903884 19 0.0121770847923283 0.0243541695846567 0.987822915207672 20 0.00360626317089572 0.00721252634179143 0.996393736829104 21 0.00104381433221669 0.00208762866443338 0.998956185667783 22 0.00118335799604857 0.00236671599209714 0.998816642003951 23 0.000394861798962403 0.000789723597924805 0.999605138201038 24 0.000144930690133487 0.000289861380266974 0.999855069309866 25 8.88749204422841e-05 0.000177749840884568 0.999911125079558 26 3.70225424280337e-05 7.40450848560674e-05 0.999962977457572 27 3.65112518286918e-05 7.30225036573836e-05 0.999963488748171 28 4.6007721506374e-05 9.2015443012748e-05 0.999953992278494 29 2.75203152527066e-05 5.50406305054133e-05 0.999972479684747 30 0.00103197425573349 0.00206394851146699 0.998968025744267 31 0.000450653080744895 0.00090130616148979 0.999549346919255 32 0.000355881994104322 0.000711763988208645 0.999644118005896 33 0.000284931690763968 0.000569863381527935 0.999715068309236 34 0.000410587652287484 0.000821175304574968 0.999589412347712 35 0.000291511162610247 0.000583022325220494 0.99970848883739 36 0.000333373989338549 0.000666747978677098 0.999666626010661 37 0.000793914150580045 0.00158782830116009 0.99920608584942 38 0.00141155665607007 0.00282311331214014 0.99858844334393 39 0.0123126075296211 0.0246252150592423 0.987687392470379 40 0.403410784417349 0.806821568834697 0.596589215582651 41 0.742313915201352 0.515372169597296 0.257686084798648 42 0.895789927507216 0.208420144985569 0.104210072492784 43 0.819531746903441 0.360936506193119 0.180468253096559 44 0.741497745488751 0.517004509022498 0.258502254511249 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 19 0.678571428571429 NOK 5% type I error level 23 0.821428571428571 NOK 10% type I error level 23 0.821428571428571 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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