*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, 18 Nov 2009 12:29:37 -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/Nov/18/t1258572728kqe26cw54eb3r2f.htm/, Retrieved Wed, 18 Nov 2009 20:32:20 +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/Nov/18/t1258572728kqe26cw54eb3r2f.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

87032 537000 88219 90390 90269 90398 87175 543000 87032 88219 90390 90269 92603 594000 87175 87032 88219 90390 93571 611000 92603 87175 87032 88219 94118 613000 93571 92603 87175 87032 92159 611000 94118 93571 92603 87175 89528 594000 92159 94118 93571 92603 89955 595000 89528 92159 94118 93571 89587 591000 89955 89528 92159 94118 89488 589000 89587 89955 89528 92159 88521 584000 89488 89587 89955 89528 86587 573000 88521 89488 89587 89955 85159 567000 86587 88521 89488 89587 84915 569000 85159 86587 88521 89488 91378 621000 84915 85159 86587 88521 92729 629000 91378 84915 85159 86587 92194 628000 92729 91378 84915 85159 89664 612000 92194 92729 91378 84915 86285 595000 89664 92194 92729 91378 86858 597000 86285 89664 92194 92729 87184 593000 86858 86285 89664 92194 86629 590000 87184 86858 86285 89664 85220 580000 86629 87184 86858 86285 84816 574000 85220 86629 87184 86858 84831 573000 84816 85220 86629 87184 84957 573000 84831 84816 85220 86629 90951 620000 84957 84831 84816 85220 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 Y[t] = + 16659.6044287766 + 0.109701069904378X[t] + 0.198692700537699Y1[t] -0.120313363550685Y2[t] -0.0163588651375638Y3[t] + 0.0456233389362317Y4[t] -154.353123603834t + 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) 16659.6044287766 4581.594147 3.6362 0.000663 0.000332 X 0.109701069904378 0.007528 14.5724 0 0 Y1 0.198692700537699 0.085059 2.3359 0.02363 0.011815 Y2 -0.120313363550685 0.09357 -1.2858 0.20455 0.102275 Y3 -0.0163588651375638 0.090113 -0.1815 0.856695 0.428348 Y4 0.0456233389362317 0.060629 0.7525 0.455352 0.227676 t -154.353123603834 21.001902 -7.3495 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.992008816501426 R-squared 0.98408149201656 Adjusted R-squared 0.982132286957363 F-TEST (value) 504.862988823807 F-TEST (DF numerator) 6 F-TEST (DF denominator) 49 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1034.89789742293 Sum Squared Residuals 52479669.24643 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 87032 84715.6324572671 2316.36754273289 2 87175 85236.9729964156 1938.02700358438 3 92603 90889.6349768715 1713.36502312846 4 93571 93581.8689132607 -10.8689132607466 5 94118 93129.697305201 988.302694798936 6 92159 92665.8918305667 -506.891830566718 7 89528 90423.3782106656 -895.378210665587 8 89955 90126.8746339073 -171.874633907262 9 89587 89992.10645652 -405.106456519972 10 89488 89447.5225262742 40.4774737257816 11 88521 88642.248553427 -121.24855342695 12 86587 87126.460070543 -539.460070542917 13 85159 86030.8020061465 -871.802006146504 14 84915 86056.106203124 -1141.10620312395 15 91378 91717.0554551917 -339.055455191664 16 92729 93688.9431970181 -959.943197018137 17 92194 92854.5790084009 -660.579008400905 18 89664 90559.3053772979 -895.305377297865 19 86285 88374.4719952029 -2089.47199520286 20 86858 88142.9203098256 -1284.92030982558 21 87184 88087.1321219173 -903.132121917253 22 86629 87539.3596094522 -910.359609452194 23 85220 85974.9642894993 -754.964289499284 24 84816 84970.0298313578 -154.029831357810 25 84831 84819.1776947198 11.8223052801574 26 84957 84714.1402483678 242.859751632230 27 90951 89681.2936870386 1269.70631296139 28 92134 91342.2743341693 791.725665830674 29 91790 90042.2330878292 1747.76691217077 30 86625 86074.4582322913 550.54176770872 31 83324 82775.9353257014 548.06467429861 32 82719 81659.4063507914 1059.59364920862 33 83614 82289.601945902 1324.39805409798 34 81640 80887.8116035885 752.188396411487 35 78665 78227.9349119507 437.065088049301 36 77828 77019.5198601155 808.480139884543 37 75728 75484.4024422887 243.597557711334 38 72187 73655.6912467192 -1468.69124671918 39 79357 79071.6481853978 285.351814602189 40 81329 81861.1289261253 -532.12892612529 41 77304 78674.9441132087 -1370.94411320872 42 75576 75559.2335622435 16.7664377564969 43 72932 73975.7422101491 -1043.74221014911 44 74291 74098.5650147176 192.434985282357 45 74988 74706.081193825 281.918806174936 46 73302 73503.8171020331 -201.817102033134 47 70483 71142.2338164929 -659.233816492898 48 69848 70352.11107992 -504.111079920071 49 66466 68166.4095091927 -1700.40950919273 50 67610 68372.9809787408 -762.980978740788 51 75091 74219.6612822005 871.33871779949 52 76207 76098.6510445142 108.348955485783 53 73454 73337.744909518 116.255090481973 54 72008 71115.5206584077 892.479341592256 55 71362 70889.3280051523 472.671994847651 56 74250 72412.3591013333 1837.64089866671 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.106882046486168 0.213764092972336 0.893117953513832 11 0.0566840752375734 0.113368150475147 0.943315924762427 12 0.078160091234358 0.156320182468716 0.921839908765642 13 0.129365120661837 0.258730241323674 0.870634879338163 14 0.133953544489635 0.26790708897927 0.866046455510365 15 0.105694099820050 0.211388199640100 0.89430590017995 16 0.170568801699373 0.341137603398747 0.829431198300627 17 0.128906604911488 0.257813209822976 0.871093395088512 18 0.233874555640255 0.46774911128051 0.766125444359745 19 0.296061251780974 0.592122503561948 0.703938748219026 20 0.449087517717165 0.89817503543433 0.550912482282836 21 0.615059118304502 0.769881763390995 0.384940881695498 22 0.609310574386985 0.78137885122603 0.390689425613015 23 0.563713508359788 0.872572983280424 0.436286491640212 24 0.572646748193549 0.854706503612903 0.427353251806451 25 0.584864113558872 0.830271772882256 0.415135886441128 26 0.58849160729312 0.82301678541376 0.41150839270688 27 0.824681336455612 0.350637327088777 0.175318663544388 28 0.921505857976787 0.156988284046426 0.0784941420232128 29 0.972085990346432 0.0558280193071357 0.0279140096535678 30 0.969763427040138 0.0604731459197238 0.0302365729598619 31 0.98076190831516 0.0384761833696792 0.0192380916848396 32 0.983714303897925 0.0325713922041504 0.0162856961020752 33 0.975126682954247 0.0497466340915063 0.0248733170457532 34 0.964308318609377 0.0713833627812451 0.0356916813906225 35 0.960922123811319 0.0781557523773628 0.0390778761886814 36 0.974270111253283 0.0514597774934335 0.0257298887467168 37 0.997261661357532 0.00547667728493497 0.00273833864246748 38 0.99766534238888 0.00466931522223823 0.00233465761111912 39 0.99595938398567 0.0080812320286593 0.00404061601432965 40 0.991857630822686 0.0162847383546279 0.00814236917731396 41 0.99735881059999 0.0052823788000181 0.00264118940000905 42 0.992437188433556 0.0151256231328883 0.00756281156644413 43 0.997670374804227 0.00465925039154655 0.00232962519577328 44 0.997798858228652 0.00440228354269653 0.00220114177134827 45 0.990794846389563 0.0184103072208730 0.00920515361043648 46 0.964507623186055 0.070984753627889 0.0354923768139445 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.162162162162162 NOK 5% type I error level 12 0.324324324324324 NOK 10% type I error level 18 0.486486486486487 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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