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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, 09 Dec 2009 08:47:20 -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/09/t12603739334pcruoo3akts3g8.htm/, Retrieved Wed, 09 Dec 2009 16:52:25 +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/09/t12603739334pcruoo3akts3g8.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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Dataseries X:

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29 38 24 25 22 24 26 42 29 24 25 22 26 35 26 29 24 25 21 25 26 26 29 24 23 24 21 26 26 29 22 22 23 21 26 26 21 27 22 23 21 26 16 17 21 22 23 21 19 30 16 21 22 23 16 30 19 16 21 22 25 34 16 19 16 21 27 37 25 16 19 16 23 36 27 25 16 19 22 33 23 27 25 16 23 33 22 23 27 25 20 33 23 22 23 27 24 37 20 23 22 23 23 40 24 20 23 22 20 35 23 24 20 23 21 37 20 23 24 20 22 43 21 20 23 24 17 42 22 21 20 23 21 33 17 22 21 20 19 39 21 17 22 21 23 40 19 21 17 22 22 37 23 19 21 17 15 44 22 23 19 21 23 42 15 22 23 19 21 43 23 15 22 23 18 40 21 23 15 22 18 30 18 21 23 15 18 30 18 18 21 23 18 31 18 18 18 21 10 18 18 18 18 18 13 24 10 18 18 18 10 22 13 10 18 18 9 26 10 13 10 18 9 28 9 10 13 10 6 23 9 9 10 13 11 17 6 9 9 10 9 12 11 6 9 9 10 9 9 11 6 9 9 19 10 9 11 6 16 21 9 10 9 11 10 18 16 9 10 9 7 18 10 16 9 10 7 15 7 10 16 9 14 24 7 7 10 16 11 18 14 7 7 10 10 19 11 14 7 7 6 30 10 11 14 7 8 33 6 10 11 14 13 35 8 6 10 11 12 36 13 8 6 10 15 47 12 13 8 6 16 46 15 12 13 8 16 43 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 S.[t] = + 14.3407345050678 + 0.234013754567813E.S[t] + 0.182528854816488`Y(t-1)`[t] + 0.221610208613917`Y(t-2)`[t] -0.0975425120261347`Y(t-3)`[t] -0.103045667145648`Y(T-4)`[t] -1.6722068286102M1[t] -2.94233377172629M2[t] -4.99006069053998M3[t] -1.85789829104282M4[t] -0.0722188170639816M5[t] -1.61978987381349M6[t] -2.58542682860624M7[t] -0.674084410588761M8[t] -1.53170254156695M9[t] -5.87072081026486M10[t] -0.623269007966605M11[t] -0.208277960241533t + 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) 14.3407345050678 4.084762 3.5108 0.001145 0.000572 E.S 0.234013754567813 0.048161 4.859 2e-05 1e-05 `Y(t-1)` 0.182528854816488 0.138719 1.3158 0.195917 0.097958 `Y(t-2)` 0.221610208613917 0.14096 1.5721 0.123995 0.061997 `Y(t-3)` -0.0975425120261347 0.141112 -0.6912 0.493507 0.246753 `Y(T-4)` -0.103045667145648 0.134927 -0.7637 0.449634 0.224817 M1 -1.6722068286102 1.938508 -0.8626 0.393617 0.196809 M2 -2.94233377172629 1.976043 -1.489 0.144529 0.072265 M3 -4.99006069053998 1.857959 -2.6858 0.010574 0.005287 M4 -1.85789829104282 1.85734 -1.0003 0.323331 0.161666 M5 -0.0722188170639816 1.723861 -0.0419 0.966797 0.483399 M6 -1.61978987381349 1.835893 -0.8823 0.383026 0.191513 M7 -2.58542682860624 1.92103 -1.3459 0.186122 0.093061 M8 -0.674084410588761 1.832372 -0.3679 0.714955 0.357478 M9 -1.53170254156695 1.792892 -0.8543 0.398145 0.199073 M10 -5.87072081026486 1.929636 -3.0424 0.004185 0.002093 M11 -0.623269007966605 2.051635 -0.3038 0.762902 0.381451 t -0.208277960241533 0.056308 -3.6989 0.000666 0.000333 Multiple Linear Regression - Regression Statistics Multiple R 0.939675191863558 R-squared 0.882989466203815 Adjusted R-squared 0.831984874549068 F-TEST (value) 17.3119603070409 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 4.01234601099532e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.52097381474045 Sum Squared Residuals 247.857050009673 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 29 26.6546888446661 2.34531115533393 2 26 26.7168368232611 -0.716836823261103 3 26 23.1716056514405 2.8283943485595 4 21 22.7058550261912 -1.70585502619122 5 23 22.9139977116284 0.0860022883715736 6 22 20.2562648535021 1.74373514649791 7 21 21.0008228338489 -0.000822833848893367 8 16 20.2797539941923 -4.27975399419228 9 19 21.0132334073926 -2.01323340739260 10 16 16.1060608790048 -0.106060879004820 11 25 22.7892920280014 2.21070797199860 12 27 25.1068542065864 1.89314579341360 13 23 25.3353957849665 -2.33539578496654 14 22 22.2993090090691 -0.299309009069098 15 23 17.8518384123786 5.1481615876214 16 20 20.9207202116500 -0.920720211650043 17 24 23.6179255684318 0.382074431568217 18 23 22.6349057636879 0.365094236312106 19 20 21.1844159243865 -1.18441592438648 20 21 22.5052780715671 -1.50527807156708 21 22 22.0465225801725 -0.0465225801725065 22 17 18.0650248633197 -1.06502486331971 23 21 20.5186353382084 0.481364661791596 24 19 21.7591851103649 -2.75918511036494 25 23 21.0187640938887 1.98123590611126 26 22 19.2502712164895 2.7497287835105 27 15 19.1191769545178 -4.11917695451782 28 23 19.8916429784952 3.10835702150476 29 21 21.2973774684784 -0.297377468478387 30 18 21.0331543983909 -3.03315439839085 31 18 16.4692745298116 1.53072547018839 32 18 16.8782280486329 1.12177195136712 33 18 16.5450645823507 1.45493541764933 34 10 9.2647265454666 0.735273454533395 35 13 14.2477520763983 -1.24775207639830 36 10 12.9694205105259 -2.96942051052588 37 9 12.9225748975468 -3.92257489754676 38 9 11.5965758237533 -2.59657582375331 39 6 7.93238249788656 -1.93238249788656 40 11 9.31127735874892 1.68872264125108 41 9 10.0694694150335 -1.06946941503350 42 10 8.64720000385403 1.35279999614597 43 9 9.37415551339281 -0.374155513392805 44 16 11.2641855224258 4.73581447757417 45 10 10.6608887648693 -0.660888764869333 46 7 6.56418771220886 0.435812287791136 47 7 8.44432055739189 -1.44432055739189 48 14 10.1645401725228 3.83545982747721 49 11 9.0685763789319 1.9314236210681 50 10 9.13700712742699 0.862992872573009 51 6 7.92499648377652 -1.92499648377652 52 8 10.1705044249146 -2.17050442491458 53 13 12.1012298364279 0.898770163572101 54 12 12.4284749805651 -0.428474980565132 55 15 14.9713311985602 0.0286688014397883 56 16 16.0725543631819 -0.0725543631819249 57 16 14.7342906652149 1.26570933478511 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0742261920587546 0.148452384117509 0.925773807941245 22 0.0272668689267298 0.0545337378534596 0.97273313107327 23 0.0268987234728617 0.0537974469457234 0.973101276527138 24 0.184956505898214 0.369913011796427 0.815043494101786 25 0.145064645525647 0.290129291051294 0.854935354474353 26 0.168535343666131 0.337070687332262 0.831464656333869 27 0.516838813978542 0.966322372042917 0.483161186021458 28 0.605295142352772 0.789409715294456 0.394704857647228 29 0.562810772645609 0.874378454708782 0.437189227354391 30 0.448590488894184 0.897180977788368 0.551409511105816 31 0.423952920152533 0.847905840305066 0.576047079847467 32 0.394213032658269 0.788426065316537 0.605786967341731 33 0.440422290002927 0.880844580005854 0.559577709997073 34 0.513897776409635 0.97220444718073 0.486102223590365 35 0.643630862922817 0.712738274154367 0.356369137077183 36 0.579234922610978 0.841530154778044 0.420765077389022 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 0 0 OK 10% type I error level 2 0.125 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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