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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: Thu, 27 Nov 2008 03:28:34 -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/Nov/27/t1227781974pqddjsjwyzg8izh.htm/, Retrieved Thu, 27 Nov 2008 10:32:54 +0000

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/Nov/27/t1227781974pqddjsjwyzg8izh.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}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1 1 16 1 29 1 56 1 51 1 50 1 37 1 20 1 47 1 49 1 39 1 30 1 0 1 14 1 36 1 72 1 41 1 43 1 44 1 18 1 56 1 57 1 49 1 31 1 17 1 22 1 49 1 65 1 55 1 48 1 50 1 15 1 60 1 56 1 40 1 31 1 20 0 27 0 14 0 67 0 64 0 46 0 60 0 22 0 65 0 58 0 42 0 32 0 25 0 20 0 27 0 72 0 68 0 51 0 53 0 18 0 54 0 67 0 40 0 45 0 25 1 36 1 50 1 64 1 50 1 43 1 51 1 12 1 58 1 50 1 50 1 31 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation S[t] = + 29.3740421455939 -1.92097701149425D[t] -17.2943007662835M1[t] -9.58572796934866M2[t] + 1.95617816091954M3[t] + 33.6647509578544M4[t] + 22.3733237547893M5[t] + 14.2485632183908M6[t] + 16.4571360153257M7[t] -15.3342911877395M8[t] + 23.7076149425287M9[t] + 23.0828544061303M10[t] + 10.1247605363985M11[t] + 0.124760536398467t + 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) 29.3740421455939 4.036746 7.2767 0 0 D -1.92097701149425 1.988609 -0.966 0.33806 0.16903 M1 -17.2943007662835 4.210532 -4.1074 0.000127 6.4e-05 M2 -9.58572796934866 4.205311 -2.2794 0.026338 0.013169 M3 1.95617816091954 4.200582 0.4657 0.64318 0.32159 M4 33.6647509578544 4.196346 8.0224 0 0 M5 22.3733237547893 4.192605 5.3364 2e-06 1e-06 M6 14.2485632183908 4.189359 3.4011 0.001221 0.00061 M7 16.4571360153257 4.186612 3.9309 0.000228 0.000114 M8 -15.3342911877395 4.184362 -3.6647 0.000538 0.000269 M9 23.7076149425287 4.182611 5.6681 0 0 M10 23.0828544061303 4.181361 5.5204 1e-06 0 M11 10.1247605363985 4.18061 2.4218 0.018589 0.009295 t 0.124760536398467 0.045742 2.7275 0.00843 0.004215 Multiple Linear Regression - Regression Statistics Multiple R 0.929166610172479 R-squared 0.863350589459415 Adjusted R-squared 0.832722273303767 F-TEST (value) 28.1879873863128 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.24059530968492 Sum Squared Residuals 3040.72078544061 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 10.2835249042145 -9.2835249042145 2 16 18.1168582375479 -2.11685823754788 3 29 29.7835249042146 -0.783524904214573 4 56 61.6168582375479 -5.6168582375479 5 51 50.4501915708812 0.549808429118768 6 50 42.4501915708812 7.54980842911877 7 37 44.7835249042146 -7.78352490421456 8 20 13.1168582375479 6.88314176245211 9 47 52.2835249042146 -5.28352490421456 10 49 51.7835249042146 -2.78352490421455 11 39 38.9501915708812 0.049808429118776 12 30 28.9501915708812 1.04980842911876 13 0 11.7806513409962 -11.7806513409962 14 14 19.6139846743295 -5.61398467432951 15 36 31.2806513409962 4.71934865900383 16 72 63.1139846743295 8.8860153256705 17 41 51.9473180076628 -10.9473180076628 18 43 43.9473180076628 -0.947318007662835 19 44 46.2806513409962 -2.28065134099617 20 18 14.6139846743295 3.38601532567049 21 56 53.7806513409962 2.21934865900383 22 57 53.2806513409962 3.71934865900383 23 49 40.4473180076628 8.55268199233716 24 31 30.4473180076628 0.552681992337164 25 17 13.2777777777778 3.72222222222221 26 22 21.1111111111111 0.888888888888888 27 49 32.7777777777778 16.2222222222222 28 65 64.6111111111111 0.388888888888888 29 55 53.4444444444444 1.55555555555555 30 48 45.4444444444444 2.55555555555556 31 50 47.7777777777778 2.22222222222222 32 15 16.1111111111111 -1.11111111111111 33 60 55.2777777777778 4.72222222222222 34 56 54.7777777777778 1.22222222222222 35 40 41.9444444444444 -1.94444444444445 36 31 31.9444444444444 -0.944444444444444 37 20 16.6958812260537 3.30411877394635 38 27 24.529214559387 2.47078544061302 39 14 36.1958812260536 -22.1958812260536 40 67 68.029214559387 -1.02921455938697 41 64 56.8625478927203 7.1374521072797 42 46 48.8625478927203 -2.86254789272031 43 60 51.1958812260536 8.80411877394636 44 22 19.5292145593870 2.47078544061303 45 65 58.6958812260536 6.30411877394637 46 58 58.1958812260536 -0.195881226053646 47 42 45.3625478927203 -3.36254789272031 48 32 35.3625478927203 -3.36254789272031 49 25 18.1930076628353 6.80699233716474 50 20 26.0263409961686 -6.02634099616858 51 27 37.6930076628352 -10.6930076628352 52 72 69.5263409961686 2.47365900383142 53 68 58.3596743295019 9.6403256704981 54 51 50.3596743295019 0.640325670498084 55 53 52.6930076628352 0.306992337164748 56 18 21.0263409961686 -3.02634099616858 57 54 60.1930076628352 -6.19300766283525 58 67 59.6930076628352 7.30699233716476 59 40 46.8596743295019 -6.85967432950192 60 45 36.8596743295019 8.14032567049808 61 25 17.7691570881226 7.23084291187738 62 36 25.6024904214559 10.3975095785441 63 50 37.2691570881226 12.7308429118774 64 64 69.102490421456 -5.10249042145594 65 50 57.9358237547893 -7.93582375478927 66 43 49.9358237547893 -6.93582375478927 67 51 52.2691570881226 -1.26915708812260 68 12 20.6024904214559 -8.60249042145594 69 58 59.7691570881226 -1.76915708812260 70 50 59.2691570881226 -9.2691570881226 71 50 46.4358237547893 3.56417624521073 72 31 36.4358237547893 -5.43582375478927 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.719449810840544 0.561100378318911 0.280550189159456 18 0.646622863615916 0.706754272768167 0.353377136384084 19 0.558523900654249 0.882952198691502 0.441476099345751 20 0.435321252222795 0.87064250444559 0.564678747777205 21 0.375008658753452 0.750017317506903 0.624991341246548 22 0.297933226083585 0.59586645216717 0.702066773916415 23 0.260188761773911 0.520377523547822 0.739811238226089 24 0.181644475754444 0.363288951508887 0.818355524245556 25 0.217196580695804 0.434393161391608 0.782803419304196 26 0.152187457399839 0.304374914799678 0.847812542600161 27 0.249209797405343 0.498419594810685 0.750790202594657 28 0.215752570381790 0.431505140763579 0.78424742961821 29 0.155997077217450 0.311994154434899 0.84400292278255 30 0.128131591660888 0.256263183321777 0.871868408339112 31 0.088732353986249 0.177464707972498 0.911267646013751 32 0.100295408065736 0.200590816131471 0.899704591934264 33 0.070778464697309 0.141556929394618 0.92922153530269 34 0.048304717719498 0.096609435438996 0.951695282280502 35 0.0487988194821404 0.0975976389642808 0.95120118051786 36 0.0340317164397354 0.0680634328794707 0.965968283560265 37 0.0212943899174693 0.0425887798349386 0.97870561008253 38 0.0130817761488505 0.0261635522977011 0.98691822385115 39 0.433214010333824 0.866428020667649 0.566785989666176 40 0.357015384426136 0.714030768852273 0.642984615573864 41 0.355255293886409 0.710510587772819 0.644744706113591 42 0.287507241560854 0.575014483121707 0.712492758439146 43 0.288882014199964 0.577764028399928 0.711117985800036 44 0.233955250277773 0.467910500555546 0.766044749722227 45 0.224963590251812 0.449927180503623 0.775036409748188 46 0.165116787857982 0.330233575715964 0.834883212142018 47 0.119739300741211 0.239478601482421 0.88026069925879 48 0.0789650477907951 0.157930095581590 0.921034952209205 49 0.0561418005189329 0.112283601037866 0.943858199481067 50 0.0854655583818656 0.170931116763731 0.914534441618134 51 0.439452595174537 0.878905190349074 0.560547404825463 52 0.323905736628951 0.647811473257902 0.676094263371049 53 0.364526792579217 0.729053585158434 0.635473207420783 54 0.250532720439116 0.501065440878231 0.749467279560884 55 0.145384966203386 0.290769932406772 0.854615033796614 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 2 0.0512820512820513 NOK 10% type I error level 5 0.128205128205128 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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