*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, 08 Dec 2010 17:03:18 +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/08/t1291828179qijau1rushh1shh.htm/, Retrieved Wed, 08 Dec 2010 18:09:49 +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/08/t1291828179qijau1rushh1shh.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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-999 -999 38,6 6654 5712 645 3 5 3 6,3 2 4,5 1 6,6 42 3 1 3 -999 -999 14 3,385 44,5 60 1 1 1 -999 -999 -999 0,92 5,7 25 5 2 3 2,1 1,8 69 2547 4603 624 3 5 4 9,1 0,7 27 10,55 179,5 180 4 4 4 15,8 3,9 19 0,023 0,3 35 1 1 1 5,2 1 30,4 160 169 392 4 5 4 10,9 3,6 28 3,3 25,6 63 1 2 1 8,3 1,4 50 52,16 440 230 1 1 1 11 1,5 7 0,42 6,4 112 5 4 4 3,2 0,7 30 465 423 281 5 5 5 7,6 2,7 -999 0,55 2,4 -999 2 1 2 -999 -999 40 187,1 419 365 5 5 5 6,3 2,1 3,5 0,075 1,2 42 1 1 1 8,6 0 50 3 25 28 2 2 2 6,6 4,1 6 0,785 3,5 42 2 2 2 9,5 1,2 10,4 0,2 5 120 2 2 2 4,8 1,3 34 1,41 17,5 -999 1 2 1 12 6,1 7 60 81 -999 1 1 1 -999 0,3 28 529 680 400 5 5 5 3,3 0,5 20 27,66 115 148 5 5 5 11 3,4 3,9 0,12 1 16 3 1 2 -999 -999 39,3 207 406 252 1 4 1 4,7 1,5 41 85 325 310 1 3 1 -999 -999 16,2 36,33 119,5 63 1 1 1 10,4 3,4 9 0,101 4 28 5 1 3 7,4 0,8 7,6 1,04 5,5 68 5 3 4 2,1 0,8 46 521 655 336 5 5 5 -999 -999 22,4 100 157 100 1 1 1 -999 -999 16,3 35 56 33 3 5 4 7,7 1,4 2,6 0,005 0,14 21,5 5 2 4 17,9 2 24 0,1 0,25 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 Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 106.032869889486 + 0.975170018219347PS[t] + 0.0384720150938441L[t] -0.00401968764009279BW[t] + 0.0207571157072056BRW[t] -0.0679549796875276Tg[t] -18.3085456520360P[t] -16.4244278016369S[t] + 3.99251851862527D[t] -50.772033723839M1[t] -32.9234928415178M2[t] -48.5522187219901M3[t] -9.55932254588741M4[t] -183.119517398206M5[t] -12.2720304320899M6[t] -45.5833528069930M7[t] -45.3053222193736M8[t] -213.805687718862M9[t] -13.3346202789063M10[t] -14.9679713918905M11[t] + 0.0174424391262367t + 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) 106.032869889486 125.798734 0.8429 0.404188 0.202094 PS 0.975170018219347 0.07359 13.2513 0 0 L 0.0384720150938441 0.117778 0.3266 0.745596 0.372798 BW -0.00401968764009279 0.091429 -0.044 0.965146 0.482573 BRW 0.0207571157072056 0.090527 0.2293 0.819781 0.409891 Tg -0.0679549796875276 0.108346 -0.6272 0.534002 0.267001 P -18.3085456520360 55.143883 -0.332 0.74157 0.370785 S -16.4244278016369 32.828458 -0.5003 0.619531 0.309766 D 3.99251851862527 69.669207 0.0573 0.954579 0.47729 M1 -50.772033723839 127.579582 -0.398 0.692722 0.346361 M2 -32.9234928415178 125.891987 -0.2615 0.795 0.3975 M3 -48.5522187219901 133.2 -0.3645 0.717353 0.358677 M4 -9.55932254588741 129.384869 -0.0739 0.941463 0.470731 M5 -183.119517398206 132.064583 -1.3866 0.17306 0.08653 M6 -12.2720304320899 123.526266 -0.0993 0.921347 0.460673 M7 -45.5833528069930 130.06506 -0.3505 0.727783 0.363892 M8 -45.3053222193736 135.641212 -0.334 0.740076 0.370038 M9 -213.805687718862 124.172198 -1.7218 0.092635 0.046317 M10 -13.3346202789063 125.974429 -0.1059 0.916216 0.458108 M11 -14.9679713918905 129.558881 -0.1155 0.908589 0.454294 t 0.0174424391262367 1.538652 0.0113 0.99101 0.495505 Multiple Linear Regression - Regression Statistics Multiple R 0.930234763075402 R-squared 0.86533671443395 Adjusted R-squared 0.799647306840754 F-TEST (value) 13.1731544877501 F-TEST (DF numerator) 20 F-TEST (DF denominator) 41 p-value 4.92150764586086e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 190.131256540752 Sum Squared Residuals 1482145.68326437 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -994.515088758222 -4.48491124177846 2 6.3 13.1740849578628 -6.87408495786285 3 -999 -950.03093021493 -48.9690697850707 4 -999 -1030.08335953264 31.0833595326379 5 2.1 -150.764310272676 152.864310272676 6 9.1 -35.923364006664 45.023364006664 7 15.8 31.9930009720007 -16.1930009720007 8 5.2 -100.147990587041 105.347990587041 9 10.9 -153.955936653129 164.855936653129 10 8.3 58.7148765227258 -50.4148765227258 11 11 -55.761341384542 66.761341384542 12 3.2 -57.8075601513587 61.0075601513587 13 7.6 42.5651527336073 -34.9651527336073 14 -999 -1069.86309073897 70.8630907389658 15 6.3 26.3548398258306 -20.0548398258306 16 8.6 35.7994466527246 -27.1994466527246 17 6.6 -136.826621445105 143.426621445105 18 9.5 26.112590548917 -16.612590548917 19 4.8 84.4364166992267 -79.6364166992267 20 12 105.880952556103 -93.8809525561028 21 -999 -274.932601810589 -724.06739818941 22 3.3 -67.144719340445 70.444719340445 23 11 30.4996608760066 -19.4996608760066 24 -999 -955.774489165013 -43.2255108349874 25 4.7 -19.5139602960413 24.2139602960413 26 -999 -932.695899671672 -66.304100328328 27 10.4 -36.1962942411197 46.5962942411197 28 7.4 -31.3224335796754 38.7224335796754 29 2.1 -239.064462387683 241.164462387683 30 -999 -913.72801693362 -85.2719830663797 31 -999 -1034.87602846697 35.876028466971 32 7.7 -47.1286849675704 54.8286849675704 33 17.9 -138.45696554878 156.35696554878 34 6.1 77.2570546730813 -71.1570546730813 35 8.2 4.55637979951042 3.64362020048958 36 8.4 8.68995344140126 -0.289953441401265 37 11.9 -21.6669511891974 33.5669511891974 38 10.8 -3.9135735399624 14.7135735399624 39 13.8 14.0736944875502 -0.273694487550242 40 14.3 54.3727540606055 -40.0727540606055 41 -999 -248.924798881353 -750.075201118647 42 15.2 26.0355909316646 -10.8355909316646 43 10 -69.3129651709281 79.3129651709281 44 11.9 17.7688597226208 -5.86885972262078 45 6.5 -231.908482230401 238.408482230401 46 7.5 -60.4970160661213 67.9970160661213 47 -999 -946.7487195331 -52.2512804668993 48 10.6 48.8251167178543 -38.2251167178543 49 7.4 25.5879708501672 -18.1879708501672 50 8.4 -9.09437304098455 17.4943730409845 51 5.7 -17.0013098573319 22.7013098573319 52 4.9 7.43359239898319 -2.53359239898319 53 -999 -1211.61980701318 212.619807013184 54 3.2 -64.4968005402973 67.6968005402973 55 -999 -979.640424033328 -19.3595759666718 56 8.1 68.5268632758874 -60.4268632758874 57 11 -153.446013757100 164.446013757100 58 4.9 21.7698042107590 -16.8698042107590 59 13.2 11.8540202421259 1.34597975787414 60 9.7 -11.0330208428841 20.7330208428841 61 12.8 12.9428766596857 -0.142876659685702 62 -999 -969.107147966278 -29.8928520337221 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 24 0.771726605269004 0.456546789461992 0.228273394730996 25 0.75478159495581 0.490436810088378 0.245218405044189 26 0.624268774760959 0.751462450478081 0.375731225239041 27 0.561434927733232 0.877130144533537 0.438565072266768 28 0.465815786072569 0.931631572145138 0.534184213927431 29 0.944682704585518 0.110634590828963 0.0553172954144817 30 0.930145598478507 0.139708803042987 0.0698544015214935 31 0.917962877095295 0.164074245809409 0.0820371229047045 32 0.87055382131194 0.258892357376119 0.129446178688059 33 0.911978506512912 0.176042986974176 0.0880214934870878 34 0.930850375761045 0.138299248477910 0.0691496242389548 35 0.868392398436788 0.263215203126424 0.131607601563212 36 0.879348786888365 0.241302426223271 0.120651213111635 37 0.790656727105735 0.418686545788531 0.209343272894265 38 0.699613222031766 0.600773555936468 0.300386777968234 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 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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