*Unverified author*

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 15:21:05 -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/t122782448369c6txfmfl0abxq.htm/, Retrieved Thu, 27 Nov 2008 22:21:32 +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/t122782448369c6txfmfl0abxq.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

123,9 0 124,9 0 112,7 0 121,9 0 100,6 0 104,3 0 120,4 0 107,5 0 102,9 0 125,6 0 107,5 0 108,8 0 128,4 0 121,1 0 119,5 0 128,7 0 108,7 0 105,5 0 119,8 0 111,3 0 110,6 0 120,1 0 97,5 0 107,7 0 127,3 0 117,2 0 119,8 0 116,2 0 111 0 112,4 0 130,6 0 109,1 0 118,8 0 123,9 0 101,6 0 112,8 0 128 0 129,6 0 125,8 0 119,5 0 115,7 0 113,6 0 129,7 0 112 0 116,8 0 127 1 112,1 1 114,2 1 121,1 1 131,6 1 125 1 120,4 1 117,7 1 117,5 1 120,6 1 127,5 1 112,3 1 124,5 1 115,2 1 105,4 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Consumtieindex[t] = + 116.251111111111 + 3.22222222222223Dummy[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) 116.251111111111 1.255154 92.619 0 0 Dummy 3.22222222222223 2.510307 1.2836 0.204388 0.102194 Multiple Linear Regression - Regression Statistics Multiple R 0.166200391832115 R-squared 0.0276225702451487 Adjusted R-squared 0.0108574421459272 F-TEST (value) 1.64762058969482 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.204387768219214 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.41982653783337 Sum Squared Residuals 4111.82177777777 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 123.9 116.251111111111 7.64888888888865 2 124.9 116.251111111111 8.6488888888889 3 112.7 116.251111111111 -3.5511111111111 4 121.9 116.251111111111 5.6488888888889 5 100.6 116.251111111111 -15.6511111111111 6 104.3 116.251111111111 -11.9511111111111 7 120.4 116.251111111111 4.1488888888889 8 107.5 116.251111111111 -8.7511111111111 9 102.9 116.251111111111 -13.3511111111111 10 125.6 116.251111111111 9.34888888888889 11 107.5 116.251111111111 -8.7511111111111 12 108.8 116.251111111111 -7.4511111111111 13 128.4 116.251111111111 12.1488888888889 14 121.1 116.251111111111 4.84888888888889 15 119.5 116.251111111111 3.24888888888889 16 128.7 116.251111111111 12.4488888888889 17 108.7 116.251111111111 -7.5511111111111 18 105.5 116.251111111111 -10.7511111111111 19 119.8 116.251111111111 3.54888888888889 20 111.3 116.251111111111 -4.95111111111111 21 110.6 116.251111111111 -5.65111111111111 22 120.1 116.251111111111 3.84888888888889 23 97.5 116.251111111111 -18.7511111111111 24 107.7 116.251111111111 -8.5511111111111 25 127.3 116.251111111111 11.0488888888889 26 117.2 116.251111111111 0.948888888888898 27 119.8 116.251111111111 3.54888888888889 28 116.2 116.251111111111 -0.0511111111111024 29 111 116.251111111111 -5.25111111111111 30 112.4 116.251111111111 -3.8511111111111 31 130.6 116.251111111111 14.3488888888889 32 109.1 116.251111111111 -7.15111111111111 33 118.8 116.251111111111 2.54888888888889 34 123.9 116.251111111111 7.6488888888889 35 101.6 116.251111111111 -14.6511111111111 36 112.8 116.251111111111 -3.45111111111111 37 128 116.251111111111 11.7488888888889 38 129.6 116.251111111111 13.3488888888889 39 125.8 116.251111111111 9.5488888888889 40 119.5 116.251111111111 3.24888888888889 41 115.7 116.251111111111 -0.551111111111102 42 113.6 116.251111111111 -2.65111111111111 43 129.7 116.251111111111 13.4488888888889 44 112 116.251111111111 -4.25111111111111 45 116.8 116.251111111111 0.548888888888892 46 127 119.473333333333 7.52666666666667 47 112.1 119.473333333333 -7.37333333333334 48 114.2 119.473333333333 -5.27333333333333 49 121.1 119.473333333333 1.62666666666666 50 131.6 119.473333333333 12.1266666666667 51 125 119.473333333333 5.52666666666667 52 120.4 119.473333333333 0.926666666666673 53 117.7 119.473333333333 -1.77333333333333 54 117.5 119.473333333333 -1.97333333333333 55 120.6 119.473333333333 1.12666666666666 56 127.5 119.473333333333 8.02666666666667 57 112.3 119.473333333333 -7.17333333333334 58 124.5 119.473333333333 5.02666666666667 59 115.2 119.473333333333 -4.27333333333333 60 105.4 119.473333333333 -14.0733333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.877425641422536 0.245148717154929 0.122574358577464 6 0.895234526371281 0.209530947257438 0.104765473628719 7 0.842332613106104 0.315334773787792 0.157667386893896 8 0.814257545165268 0.371484909669464 0.185742454834732 9 0.849589659591862 0.300820680816275 0.150410340408138 10 0.87390667714422 0.25218664571156 0.12609332285578 11 0.8524417671624 0.295116465675202 0.147558232837601 12 0.816007647125905 0.367984705748191 0.183992352874095 13 0.883400381074557 0.233199237850885 0.116599618925443 14 0.853912374563657 0.292175250872687 0.146087625436343 15 0.807988275657059 0.384023448685882 0.192011724342941 16 0.860597896396186 0.278804207207629 0.139402103603814 17 0.844582504866664 0.310834990266672 0.155417495133336 18 0.861759954096877 0.276480091806246 0.138240045903123 19 0.822002812526786 0.355994374946427 0.177997187473214 20 0.78147610387627 0.437047792247458 0.218523896123729 21 0.743001898948659 0.513996202102682 0.256998101051341 22 0.691632765238564 0.616734469522872 0.308367234761436 23 0.887353044296858 0.225293911406284 0.112646955703142 24 0.890112364715639 0.219775270568723 0.109887635284361 25 0.912205265893139 0.175589468213723 0.0877947341068615 26 0.8791079209035 0.241784158192999 0.120892079096499 27 0.844029318472098 0.311941363055803 0.155970681527902 28 0.795796004065426 0.408407991869147 0.204203995934574 29 0.768966328271732 0.462067343456535 0.231033671728268 30 0.730592026586673 0.538815946826653 0.269407973413327 31 0.81976222279849 0.360475554403021 0.180237777201511 32 0.819788166835857 0.360423666328287 0.180211833164143 33 0.76865968876364 0.462680622472722 0.231340311236361 34 0.74458585429136 0.510828291417279 0.255414145708639 35 0.894782485740328 0.210435028519343 0.105217514259672 36 0.88406451388904 0.231870972221921 0.115935486110961 37 0.89476718702032 0.210465625959359 0.105232812979679 38 0.924504942809165 0.15099011438167 0.075495057190835 39 0.92425625754291 0.151487484914181 0.0757437424570907 40 0.892215341092106 0.215569317815789 0.107784658907894 41 0.849538352052394 0.300923295895211 0.150461647947606 42 0.812604476684556 0.374791046630888 0.187395523315444 43 0.888349631541048 0.223300736917904 0.111650368458952 44 0.849127648031359 0.301744703937282 0.150872351968641 45 0.787349122499073 0.425301755001853 0.212650877500927 46 0.770979110763306 0.458041778473387 0.229020889236694 47 0.763363094924488 0.473273810151024 0.236636905075512 48 0.715258328433392 0.569483343133215 0.284741671566608 49 0.621810139034386 0.756379721931228 0.378189860965614 50 0.746796599554198 0.506406800891604 0.253203400445802 51 0.712968913350225 0.57406217329955 0.287031086649775 52 0.606978651897119 0.786042696205761 0.393021348102881 53 0.473718546966482 0.947437093932964 0.526281453033518 54 0.333560413163114 0.667120826326229 0.666439586836886 55 0.214344695290819 0.428689390581638 0.78565530470918 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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