q3

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 23 Nov 2008 08:48:09 -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/23/t1227455379tzeck19eynyt6mp.htm/, Retrieved Sun, 23 Nov 2008 15:49:48 +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/23/t1227455379tzeck19eynyt6mp.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:

» Textbox « » Textfile « » CSV «

1515 0 1510 0 1225 0 1577 0 1417 0 1224 0 1693 0 1633 0 1639 0 1914 0 1586 0 1552 0 2081 0 1500 0 1437 0 1470 0 1849 0 1387 0 1592 0 1589 0 1798 0 1935 0 1887 0 2027 0 2080 0 1556 0 1682 0 1785 0 1869 0 1781 0 2082 0 2570 1 1862 1 1936 1 1504 1 1765 1 1607 1 1577 1 1493 1 1615 1 1700 1 1335 1 1523 1 1623 1 1540 1 1637 1 1524 1 1419 1 1821 1 1593 1 1357 1 1263 1 1750 1 1405 1 1393 1 1639 1 1679 1 1551 1 1744 1 1429 1 1784 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Gebouwen[t] = + 1673.29032258065 -52.0236559139788Dummy[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) 1673.29032258065 43.134805 38.7921 0 0 Dummy -52.0236559139788 61.508074 -0.8458 0.40108 0.20054 Multiple Linear Regression - Regression Statistics Multiple R 0.109452487267922 R-squared 0.0119798469691347 Adjusted R-squared -0.00476625731952396 F-TEST (value) 0.715381127612351 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.401080470251237 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 240.164430034128 Sum Squared Residuals 3403058.25376344 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1515 1673.29032258064 -158.290322580638 2 1510 1673.29032258065 -163.290322580645 3 1225 1673.29032258065 -448.290322580645 4 1577 1673.29032258065 -96.2903225806454 5 1417 1673.29032258065 -256.290322580645 6 1224 1673.29032258065 -449.290322580645 7 1693 1673.29032258065 19.7096774193546 8 1633 1673.29032258065 -40.2903225806454 9 1639 1673.29032258065 -34.2903225806454 10 1914 1673.29032258065 240.709677419355 11 1586 1673.29032258065 -87.2903225806454 12 1552 1673.29032258065 -121.290322580645 13 2081 1673.29032258065 407.709677419355 14 1500 1673.29032258065 -173.290322580645 15 1437 1673.29032258065 -236.290322580645 16 1470 1673.29032258065 -203.290322580645 17 1849 1673.29032258065 175.709677419355 18 1387 1673.29032258065 -286.290322580645 19 1592 1673.29032258065 -81.2903225806454 20 1589 1673.29032258065 -84.2903225806454 21 1798 1673.29032258065 124.709677419355 22 1935 1673.29032258065 261.709677419355 23 1887 1673.29032258065 213.709677419355 24 2027 1673.29032258065 353.709677419355 25 2080 1673.29032258065 406.709677419355 26 1556 1673.29032258065 -117.290322580645 27 1682 1673.29032258065 8.70967741935458 28 1785 1673.29032258065 111.709677419355 29 1869 1673.29032258065 195.709677419355 30 1781 1673.29032258065 107.709677419355 31 2082 1673.29032258065 408.709677419355 32 2570 1621.26666666667 948.733333333333 33 1862 1621.26666666667 240.733333333333 34 1936 1621.26666666667 314.733333333333 35 1504 1621.26666666667 -117.266666666667 36 1765 1621.26666666667 143.733333333333 37 1607 1621.26666666667 -14.2666666666667 38 1577 1621.26666666667 -44.2666666666667 39 1493 1621.26666666667 -128.266666666667 40 1615 1621.26666666667 -6.26666666666667 41 1700 1621.26666666667 78.7333333333333 42 1335 1621.26666666667 -286.266666666667 43 1523 1621.26666666667 -98.2666666666667 44 1623 1621.26666666667 1.73333333333333 45 1540 1621.26666666667 -81.2666666666667 46 1637 1621.26666666667 15.7333333333333 47 1524 1621.26666666667 -97.2666666666667 48 1419 1621.26666666667 -202.266666666667 49 1821 1621.26666666667 199.733333333333 50 1593 1621.26666666667 -28.2666666666667 51 1357 1621.26666666667 -264.266666666667 52 1263 1621.26666666667 -358.266666666667 53 1750 1621.26666666667 128.733333333333 54 1405 1621.26666666667 -216.266666666667 55 1393 1621.26666666667 -228.266666666667 56 1639 1621.26666666667 17.7333333333333 57 1679 1621.26666666667 57.7333333333333 58 1551 1621.26666666667 -70.2666666666667 59 1744 1621.26666666667 122.733333333333 60 1429 1621.26666666667 -192.266666666667 61 1784 1621.26666666667 162.733333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.281617307471888 0.563234614943776 0.718382692528112 6 0.309050892092329 0.618101784184659 0.690949107907671 7 0.371750584585843 0.743501169171686 0.628249415414157 8 0.31839156304543 0.63678312609086 0.68160843695457 9 0.263150101713527 0.526300203427053 0.736849898286473 10 0.473776236529545 0.94755247305909 0.526223763470455 11 0.375938216723522 0.751876433447044 0.624061783276478 12 0.289217434206278 0.578434868412557 0.710782565793722 13 0.618767288243857 0.762465423512287 0.381232711756143 14 0.55396358822042 0.89207282355916 0.44603641177958 15 0.522810134650467 0.954379730699066 0.477189865349533 16 0.481378601247236 0.96275720249447 0.518621398752764 17 0.490689607900876 0.98137921580175 0.509310392099124 18 0.519527910625617 0.960944178748766 0.480472089374383 19 0.461996112335491 0.923992224670982 0.538003887664509 20 0.412807842017376 0.825615684034752 0.587192157982624 21 0.391375386739526 0.782750773479051 0.608624613260474 22 0.440457487461972 0.880914974923943 0.559542512538028 23 0.440439740612647 0.880879481225294 0.559560259387353 24 0.527409167550815 0.94518166489837 0.472590832449185 25 0.639291137413728 0.721417725172543 0.360708862586272 26 0.60786853289421 0.784262934211579 0.392131467105790 27 0.552035308062644 0.895929383874712 0.447964691937356 28 0.497111087560632 0.994222175121265 0.502888912439368 29 0.45616972312177 0.91233944624354 0.54383027687823 30 0.4189256508217 0.8378513016434 0.5810743491783 31 0.455841896420356 0.911683792840711 0.544158103579644 32 0.960509295521564 0.0789814089568712 0.0394907044784356 33 0.985040171634968 0.0299196567300643 0.0149598283650321 34 0.994583439058368 0.0108331218832645 0.00541656094163223 35 0.996313892511455 0.00737221497708944 0.00368610748854472 36 0.99632577017489 0.00734845965021947 0.00367422982510974 37 0.994863786862759 0.0102724262744825 0.00513621313724126 38 0.992426516043154 0.0151469679136924 0.00757348395684622 39 0.989924448568648 0.0201511028627049 0.0100755514313524 40 0.984040521700343 0.0319189565993134 0.0159594782996567 41 0.978475800906403 0.0430483981871949 0.0215241990935974 42 0.984213078929497 0.0315738421410064 0.0157869210705032 43 0.974807648878385 0.0503847022432310 0.0251923511216155 44 0.95966823849949 0.0806635230010182 0.0403317615005091 45 0.936960514925553 0.126078970148894 0.063039485074447 46 0.906222834131421 0.187554331737157 0.0937771658685787 47 0.862774930775764 0.274450138448471 0.137225069224236 48 0.83507218735041 0.329855625299179 0.164927812649590 49 0.854321677018413 0.291356645963175 0.145678322981587 50 0.786123160354106 0.427753679291788 0.213876839645894 51 0.775714916956018 0.448570166087965 0.224285083043982 52 0.871777531116893 0.256444937766215 0.128222468883107 53 0.839795810578758 0.320408378842484 0.160204189421242 54 0.821390962545115 0.357218074909770 0.178609037454885 55 0.848645902850776 0.302708194298449 0.151354097149224 56 0.708587261760392 0.582825476479216 0.291412738239608 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0384615384615385 NOK 5% type I error level 10 0.192307692307692 NOK 10% type I error level 13 0.25 NOK

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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