*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: Wed, 22 Dec 2010 20:24:38 +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/22/t129304965254yjqkdejfz0x9f.htm/, Retrieved Wed, 22 Dec 2010 21:27:43 +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/22/t129304965254yjqkdejfz0x9f.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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6.3 0 3 2.1 3.40602894496361 4 9.1 1.02325245963371 4 15.8 -1.63827216398241 1 5.2 2.20411998265592 4 10.9 0.51851393987789 1 8.3 1.71733758272386 1 11 -0.37161106994969 4 3.2 2.66745295288995 5 7.6 -0.25963731050576 2 6.3 -1.1249387366083 1 8.6 0.47712125471966 2 6.6 -0.10513034325475 2 9.5 -0.69897000433602 2 4.8 0.14921911265538 1 12 1.77815125038364 1 3.3 1.44185217577329 5 11 -0.92081875395238 2 4.7 1.92941892571429 1 10.4 -0.99567862621736 3 7.4 0.01703333929878 4 2.1 2.71683772329952 5 7.7 -2.30102999566398 4 17.9 -2 1 6.1 1.79239168949825 1 8.2 -0.91364016932525 1 8.4 0.13033376849501 3 11.9 -1.63827216398241 3 10.8 -1.31875876262441 3 13.8 0.23044892137827 1 14.3 0.54406804435028 1 15.2 -0.31875876262441 2 10 1 4 11.9 0.20951501454263 2 6.5 2.28330122870355 4 7.5 0.39794000867204 5 10.6 -0.55284196865778 3 7.4 0.62685341466673 1 8.4 0.83250891270624 2 5.7 -0.1249387366083 2 4.9 0.55630250076729 3 3.2 1.74429298312268 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation a[t] = + 11.0993680337852 -1.36670460234400d[t] -0.799355917712502c[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) 11.0993680337852 0.771044 14.3952 0 0 d -1.36670460234400 0.286257 -4.7744 1.3e-05 6e-06 c -0.799355917712502 0.279091 -2.8641 0.005843 0.002922 Multiple Linear Regression - Regression Statistics Multiple R 0.680046885325777 R-squared 0.462463766241290 Adjusted R-squared 0.443602845758529 F-TEST (value) 24.5196816700419 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 2.07310217881229e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.72841235785912 Sum Squared Residuals 424.321337687545 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 8.70130028064773 -2.40130028064773 2 2.1 3.24690892813658 -1.14690892813658 3 9.1 6.50346051699402 2.59653948300598 4 15.8 12.5390462224796 3.26095377752045 5 5.2 4.88956343852101 0.310436561478993 6 10.9 9.5913567280621 1.3086432719379 7 8.3 7.95291893798572 0.347081062014285 8 11 8.40982692251745 2.59017307748255 9 3.2 3.45696821797194 -0.256968217971941 10 7.6 9.85550370556867 -2.25550370556867 11 6.3 11.8374710647503 -5.53747106475034 12 8.6 8.84857238365873 -0.248572383658729 13 6.6 9.6443383223325 -3.04433832233250 14 9.5 10.4559417201867 -0.955941720186674 15 4.8 10.0960736680489 -5.29607366804894 16 12 7.86980461850968 4.13019538149032 17 3.3 5.13200244069366 -1.83200244069366 18 11 10.7591434273116 0.240856572688385 19 4.7 7.6630663904494 -2.9630663904494 20 10.4 10.0620988415545 0.337901158445455 21 7.4 7.8786648197223 -0.478664819722298 22 2.1 3.38947382496748 -1.28947382496748 23 7.7 11.0467726481408 -3.34677264814078 24 17.9 13.0334213207607 4.86657867923927 25 6.1 7.85034214483234 -1.75034214483234 26 8.2 11.5486883403759 -3.3486883403759 27 8.4 8.52317251940476 -0.123172519404762 28 11.9 10.9403343870546 0.95966561294545 29 10.8 10.503653950908 0.296346049092014 30 13.8 9.98505651461984 3.81494348538016 31 14.3 9.5564318158709 4.7435681841291 32 15.2 9.9363052662765 5.26369473372351 33 10 6.53523976059123 3.46476023940877 34 11.9 9.21431106372465 2.68568893627535 35 6.5 4.78134606512838 1.71865393487162 36 7.5 6.55872200391384 0.941277996086162 37 10.6 9.45687194358123 1.14312805641877 38 7.4 9.44328866925266 -2.04328866925266 39 8.4 8.36286243587221 0.0371375641277857 40 5.7 9.67141054469384 -3.97141054469384 41 4.9 7.9409990925536 -3.04099909255360 42 3.2 4.71865519735262 -1.51865519735262 43 8.1 11.1705625078292 -3.07056250782917 44 11 9.56319317130122 1.43680682869878 45 4.9 8.28988120013017 -3.38988120013017 46 13.2 10.8440812574913 2.3559187425087 47 9.7 7.05156159410421 2.64843840589579 48 12.8 9.5564318158709 3.24356818412909 49 6.3 8.70130028064773 -2.40130028064773 50 2.1 3.24690892813659 -1.14690892813659 51 9.1 6.50346051699402 2.59653948300598 52 15.8 12.5390462224796 3.26095377752045 53 5.2 4.88956343852101 0.310436561478993 54 10.9 9.5913567280621 1.3086432719379 55 8.3 7.95291893798572 0.347081062014285 56 11 8.40982692251745 2.59017307748255 57 3.2 3.45696821797194 -0.256968217971941 58 7.6 9.85550370556867 -2.25550370556867 59 6.3 11.8374710647503 -5.53747106475034 60 8.6 8.84857238365873 -0.248572383658729 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.492518089379036 0.985036178758071 0.507481910620964 7 0.321597751180789 0.643195502361579 0.67840224881921 8 0.222111506555021 0.444223013110042 0.777888493444979 9 0.127774050568543 0.255548101137086 0.872225949431457 10 0.212277877167884 0.424555754335767 0.787722122832116 11 0.601617882457214 0.796764235085571 0.398382117542786 12 0.493996175374081 0.987992350748163 0.506003824625919 13 0.489169779636304 0.978339559272607 0.510830220363696 14 0.394677994739084 0.789355989478168 0.605322005260916 15 0.535989105922567 0.928021788154865 0.464010894077433 16 0.708359992720583 0.583280014558834 0.291640007279417 17 0.66040527336712 0.67918945326576 0.33959472663288 18 0.587806950528967 0.824386098942067 0.412193049471033 19 0.585809772957431 0.828380454085138 0.414190227042569 20 0.50745604554766 0.98508790890468 0.49254395445234 21 0.425490377218784 0.850980754437569 0.574509622781216 22 0.363176921550753 0.726353843101507 0.636823078449247 23 0.376234705887278 0.752469411774557 0.623765294112722 24 0.576751793973335 0.84649641205333 0.423248206026665 25 0.52640124503341 0.94719750993318 0.47359875496659 26 0.554128741502553 0.891742516994893 0.445871258497447 27 0.478275331423737 0.956550662847474 0.521724668576263 28 0.414010911061727 0.828021822123453 0.585989088938273 29 0.341969056862355 0.68393811372471 0.658030943137645 30 0.410676742770202 0.821353485540404 0.589323257229798 31 0.55530387453944 0.88939225092112 0.44469612546056 32 0.738350851327407 0.523298297345185 0.261649148672593 33 0.769435695974747 0.461128608050507 0.230564304025253 34 0.770779194640022 0.458441610719955 0.229220805359978 35 0.731982932879 0.536034134242 0.268017067121 36 0.669081601247107 0.661836797505785 0.330918398752892 37 0.609867248308208 0.780265503383584 0.390132751691792 38 0.566985773301491 0.866028453397018 0.433014226698509 39 0.485400023820038 0.970800047640076 0.514599976179962 40 0.556050138823183 0.887899722353633 0.443949861176817 41 0.567223304686135 0.86555339062773 0.432776695313865 42 0.509844643019706 0.980310713960588 0.490155356980294 43 0.536196754592054 0.927606490815892 0.463803245407946 44 0.463959673971035 0.927919347942071 0.536040326028965 45 0.533832022487078 0.932335955025843 0.466167977512922 46 0.484746938746335 0.96949387749267 0.515253061253665 47 0.450628857729868 0.901257715459735 0.549371142270132 48 0.50600382462592 0.98799235074816 0.49399617537408 49 0.495917461454193 0.991834922908386 0.504082538545807 50 0.405384111326961 0.810768222653922 0.594615888673039 51 0.345210889945505 0.69042177989101 0.654789110054495 52 0.509413161146966 0.981173677706068 0.490586838853034 53 0.371660196562596 0.743320393125192 0.628339803437404 54 0.349185953069378 0.698371906138755 0.650814046930622 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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