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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: Sat, 04 Dec 2010 10:22:32 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/04/t1291458153do3krugnq4jd71j.htm/, Retrieved Sat, 04 Dec 2010 11:22:33 +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/2010/Dec/04/t1291458153do3krugnq4jd71j.htm/}, year = {2010}, } @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 = {2010}, 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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14731798,37 0 16471559,62 0 15213975,95 0 17637387,4 0 17972385,83 0 16896235,55 0 16697955,94 0 19691579,52 0 15930700,75 0 17444615,98 0 17699369,88 0 15189796,81 0 15672722,75 0 17180794,3 0 17664893,45 0 17862884,98 0 16162288,88 0 17463628,82 0 16772112,17 0 19106861,48 0 16721314,25 0 18161267,85 0 18509941,2 0 17802737,97 0 16409869,75 0 17967742,04 0 20286602,27 0 19537280,81 0 18021889,62 0 20194317,23 0 19049596,62 0 20244720,94 0 21473302,24 0 19673603,19 0 21053177,29 0 20159479,84 0 18203628,31 0 21289464,94 0 20432335,71 1 17180395,07 1 15816786,32 1 15071819,75 1 14521120,61 1 15668789,39 1 14346884,11 1 13881008,13 1 15465943,69 1 14238232,92 1 13557713,21 1 16127590,29 1 16793894,2 1 16014007,43 1 16867867,15 1 16014583,21 1 15878594,85 1 18664899,14 1 17962530,06 1 17332692,2 1 19542066,35 1 17203555,19 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 18005881.1786842 -1706639.86141148X[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) 18005881.1786842 287050.535243 62.7272 0 0 X -1706639.86141148 474048.357094 -3.6001 0.00066 0.00033 Multiple Linear Regression - Regression Statistics Multiple R 0.427375260674085 R-squared 0.182649613436242 Adjusted R-squared 0.168557365392040 F-TEST (value) 12.9609990445336 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.000659816856859119 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1769498.33901066 Sum Squared Residuals 181605213562166 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14731798.37 18005881.1786842 -3274082.80868423 2 16471559.62 18005881.1786842 -1534321.55868421 3 15213975.95 18005881.1786842 -2791905.22868421 4 17637387.4 18005881.1786842 -368493.778684211 5 17972385.83 18005881.1786842 -33495.3486842115 6 16896235.55 18005881.1786842 -1109645.62868421 7 16697955.94 18005881.1786842 -1307925.23868421 8 19691579.52 18005881.1786842 1685698.34131579 9 15930700.75 18005881.1786842 -2075180.42868421 10 17444615.98 18005881.1786842 -561265.198684209 11 17699369.88 18005881.1786842 -306511.298684211 12 15189796.81 18005881.1786842 -2816084.36868421 13 15672722.75 18005881.1786842 -2333158.42868421 14 17180794.3 18005881.1786842 -825086.878684209 15 17664893.45 18005881.1786842 -340987.728684210 16 17862884.98 18005881.1786842 -142996.198684209 17 16162288.88 18005881.1786842 -1843592.29868421 18 17463628.82 18005881.1786842 -542252.358684209 19 16772112.17 18005881.1786842 -1233769.00868421 20 19106861.48 18005881.1786842 1100980.30131579 21 16721314.25 18005881.1786842 -1284566.92868421 22 18161267.85 18005881.1786842 155386.671315792 23 18509941.2 18005881.1786842 504060.021315789 24 17802737.97 18005881.1786842 -203143.208684211 25 16409869.75 18005881.1786842 -1596011.42868421 26 17967742.04 18005881.1786842 -38139.1386842106 27 20286602.27 18005881.1786842 2280721.09131579 28 19537280.81 18005881.1786842 1531399.63131579 29 18021889.62 18005881.1786842 16008.4413157913 30 20194317.23 18005881.1786842 2188436.05131579 31 19049596.62 18005881.1786842 1043715.44131579 32 20244720.94 18005881.1786842 2238839.76131579 33 21473302.24 18005881.1786842 3467421.06131579 34 19673603.19 18005881.1786842 1667722.01131579 35 21053177.29 18005881.1786842 3047296.11131579 36 20159479.84 18005881.1786842 2153598.66131579 37 18203628.31 18005881.1786842 197747.131315789 38 21289464.94 18005881.1786842 3283583.76131579 39 20432335.71 16299241.3172727 4133094.39272727 40 17180395.07 16299241.3172727 881153.752727273 41 15816786.32 16299241.3172727 -482454.997272727 42 15071819.75 16299241.3172727 -1227421.56727273 43 14521120.61 16299241.3172727 -1778120.70727273 44 15668789.39 16299241.3172727 -630451.927272727 45 14346884.11 16299241.3172727 -1952357.20727273 46 13881008.13 16299241.3172727 -2418233.18727273 47 15465943.69 16299241.3172727 -833297.627272728 48 14238232.92 16299241.3172727 -2061008.39727273 49 13557713.21 16299241.3172727 -2741528.10727273 50 16127590.29 16299241.3172727 -171651.027272728 51 16793894.2 16299241.3172727 494652.882727272 52 16014007.43 16299241.3172727 -285233.887272728 53 16867867.15 16299241.3172727 568625.832727271 54 16014583.21 16299241.3172727 -284658.107272726 55 15878594.85 16299241.3172727 -420646.467272728 56 18664899.14 16299241.3172727 2365657.82272727 57 17962530.06 16299241.3172727 1663288.74272727 58 17332692.2 16299241.3172727 1033450.88272727 59 19542066.35 16299241.3172727 3242825.03272727 60 17203555.19 16299241.3172727 904313.872727274 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.558928121125516 0.882143757748968 0.441071878874484 6 0.402143399451635 0.804286798903269 0.597856600548365 7 0.268627842044029 0.537255684088058 0.731372157955971 8 0.527754995423217 0.944490009153566 0.472245004576783 9 0.459909248349947 0.919818496699893 0.540090751650053 10 0.362388937576197 0.724777875152395 0.637611062423803 11 0.284032743789707 0.568065487579414 0.715967256210293 12 0.327673803363768 0.655347606727535 0.672326196636232 13 0.317576191948029 0.635152383896058 0.682423808051971 14 0.252118609168872 0.504237218337744 0.747881390831128 15 0.205514663205218 0.411029326410437 0.794485336794782 16 0.169875929509525 0.33975185901905 0.830124070490475 17 0.156098108748587 0.312196217497175 0.843901891251413 18 0.123282874372760 0.246565748745521 0.87671712562724 19 0.102047209246263 0.204094418492525 0.897952790753737 20 0.134482539585410 0.268965079170819 0.86551746041459 21 0.120726246782729 0.241452493565458 0.87927375321727 22 0.106584769221271 0.213169538442542 0.893415230778729 23 0.100523814167685 0.20104762833537 0.899476185832315 24 0.0844272241267162 0.168854448253432 0.915572775873284 25 0.104911328523186 0.209822657046373 0.895088671476814 26 0.0981323858819557 0.196264771763911 0.901867614118044 27 0.188466701086481 0.376933402172961 0.81153329891352 28 0.211647474682694 0.423294949365389 0.788352525317305 29 0.201995655240509 0.403991310481019 0.79800434475949 30 0.256072528637631 0.512145057275262 0.743927471362369 31 0.244753376909895 0.48950675381979 0.755246623090105 32 0.278332798498568 0.556665596997135 0.721667201501432 33 0.414473312652171 0.828946625304343 0.585526687347829 34 0.387468491774739 0.774936983549477 0.612531508225261 35 0.441602871463715 0.88320574292743 0.558397128536285 36 0.418782136882781 0.837564273765563 0.581217863117219 37 0.411454953198731 0.822909906397462 0.588545046801269 38 0.434572551522545 0.86914510304509 0.565427448477455 39 0.656716945496245 0.68656610900751 0.343283054503755 40 0.642980462542198 0.714039074915605 0.357019537457802 41 0.608319390461626 0.783361219076747 0.391680609538374 42 0.585301839045382 0.829396321909237 0.414698160954618 43 0.589914416449307 0.820171167101386 0.410085583550693 44 0.513337205934965 0.97332558813007 0.486662794065035 45 0.527858299533254 0.944283400933492 0.472141700466746 46 0.613480747177511 0.773038505644978 0.386519252822489 47 0.550177358674601 0.899645282650798 0.449822641325399 48 0.62813311228063 0.743733775438741 0.371866887719370 49 0.87718512138138 0.245629757237240 0.122814878618620 50 0.840813360778591 0.318373278442818 0.159186639221409 51 0.766317479612796 0.467365040774408 0.233682520387204 52 0.731393061606144 0.537213876787711 0.268606938393856 53 0.625891557918294 0.748216884163412 0.374108442081706 54 0.613702493947625 0.772595012104749 0.386297506052375 55 0.731705454399314 0.536589091201371 0.268294545600686 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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