*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: Fri, 03 Dec 2010 18:58:22 +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/03/t1291402790x9av7tggcml7y71.htm/, Retrieved Fri, 03 Dec 2010 20:00:00 +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/03/t1291402790x9av7tggcml7y71.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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1 162556 1081 213118 6282929 1 29790 309 81767 4324047 1 87550 458 153198 4108272 0 84738 588 -26007 -1212617 1 54660 299 126942 1485329 1 42634 156 157214 1779876 0 40949 481 129352 1367203 1 42312 323 234817 2519076 1 37704 452 60448 912684 1 16275 109 47818 1443586 0 25830 115 245546 1220017 0 12679 110 48020 984885 1 18014 239 -1710 1457425 0 43556 247 32648 -572920 1 24524 497 95350 929144 0 6532 103 151352 1151176 0 7123 109 288170 790090 1 20813 502 114337 774497 1 37597 248 37884 990576 0 17821 373 122844 454195 1 12988 119 82340 876607 1 22330 84 79801 711969 0 13326 102 165548 702380 0 16189 295 116384 264449 0 7146 105 134028 450033 0 15824 64 63838 541063 1 26088 267 74996 588864 0 11326 129 31080 -37216 0 8568 37 32168 783310 0 14416 361 49857 467359 1 3369 28 87161 688779 1 11819 85 106113 608419 1 6620 44 80570 696348 1 4519 49 102129 597793 0 2220 22 301670 821730 0 18562 155 102313 377934 0 10327 91 88577 651939 1 5336 81 112477 697458 1 2365 79 191778 70 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Wealth[t] = -504114.977829084 + 662967.306012224Group[t] + 24.5611272824609Costs[t] -41.5957333099101Trades[t] + 5.32130251682934Dividends[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) -504114.977829084 268975.73522 -1.8742 0.067552 0.033776 Group 662967.306012224 233076.812238 2.8444 0.006727 0.003364 Costs 24.5611272824609 6.190525 3.9675 0.000264 0.000132 Trades -41.5957333099101 789.29099 -0.0527 0.958209 0.479105 Dividends 5.32130251682934 1.690371 3.148 0.00295 0.001475 Multiple Linear Regression - Regression Statistics Multiple R 0.76894626336554 R-squared 0.591278355943827 Adjusted R-squared 0.554121842847811 F-TEST (value) 15.9131820151130 F-TEST (DF numerator) 4 F-TEST (DF denominator) 44 p-value 3.96084618436987e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 792391.601716665 Sum Squared Residuals 27626915820728.5 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6282929 5240511.29678447 1042417.70321553 2 4324047 1312782.17122847 3011264.82877153 3 4108272 3105341.07887987 1002930.92112013 4 -1212617 1414296.42009068 -2626913.42009068 5 1485329 2164423.20527414 -679094.205274138 6 1779876 2036085.74822804 -256209.748228038 7 1367203 1169952.19869525 197250.801304752 8 2519076 2434179.61699384 84896.383006163 9 912684 1387765.89432226 -475081.894322265 10 1443586 808504.783524156 635081.216475844 11 1220017 1432139.97834362 -212122.978343617 12 984885 58248.9711792924 926636.028820708 13 1457425 582255.667484544 875169.332515456 14 -572920 729125.220527678 -1302045.22052768 15 929144 1247902.52918286 -318758.529182862 16 1151176 457423.723576184 693752.276423816 17 790090 1199739.74314781 -409649.743147815 18 774497 1257583.77805814 -483086.778058139 19 990576 1273553.51330853 -282977.513308526 20 454195 571763.749324438 -117568.749324438 21 876607 911058.40629959 -34451.4062995899 22 711969 1128453.52094796 -416484.520947956 23 702380 699874.828595442 2505.17140455813 24 264449 500548.842538917 -236099.842538917 25 450033 380234.819459443 69798.1805405567 26 541063 221579.483426094 319483.516573906 27 588864 1187573.35948637 -598709.359486366 28 -37216 -65915.4176018545 28699.4176018545 29 783310 -124038.622044060 907348.62204406 30 467359 100246.352931555 367112.647068445 31 688779 704244.134134435 -15465.1341344350 32 608419 1010264.02817151 -401845.028171514 33 696348 748354.122308335 -52006.1223083347 34 597793 811265.176181658 -213472.176181658 35 821730 1154772.94885707 -333042.948857067 36 377934 489779.752529279 -111845.752529279 37 651939 217087.58491888 434851.41508112 38 697458 885065.392149662 -187607.392149662 39 700368 1234162.08534717 -533794.085347173 40 225986 14454.0938063610 211531.906193639 41 348695 334000.380231905 14694.6197680950 42 373683 343506.211642966 30176.7883570342 43 501709 96820.1978022888 404888.802197711 44 413743 285587.325254383 128155.674745617 45 379825 -25009.0554696691 404834.055469669 46 336260 789241.854339624 -452981.854339624 47 636765 1309336.69349311 -672571.693493115 48 481231 1058393.94387125 -577162.94387125 49 469107 261538.268236057 207568.731763943 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.99999776552202 4.46895596018079e-06 2.23447798009039e-06 9 0.999999997104694 5.79061141253223e-09 2.89530570626611e-09 10 0.999999997833657 4.33268589712414e-09 2.16634294856207e-09 11 0.999999997810177 4.37964600785177e-09 2.18982300392588e-09 12 0.999999999852327 2.95345996691483e-10 1.47672998345741e-10 13 0.999999999983704 3.25922187753303e-11 1.62961093876652e-11 14 0.999999999999971 5.76174671813783e-14 2.88087335906892e-14 15 0.99999999999998 3.88583823724936e-14 1.94291911862468e-14 16 1 1.16482526544679e-15 5.82412632723397e-16 17 0.999999999999997 5.21714082293867e-15 2.60857041146933e-15 18 0.999999999999992 1.53111720049049e-14 7.65558600245243e-15 19 0.999999999999984 3.19786807605004e-14 1.59893403802502e-14 20 0.99999999999989 2.18734511392418e-13 1.09367255696209e-13 21 0.99999999999981 3.80806001867231e-13 1.90403000933615e-13 22 0.999999999999147 1.7057508495589e-12 8.5287542477945e-13 23 0.999999999996103 7.79313730849583e-12 3.89656865424791e-12 24 0.999999999985118 2.97633028648754e-11 1.48816514324377e-11 25 0.999999999914337 1.71325549419838e-10 8.5662774709919e-11 26 0.999999999631446 7.37107824852936e-10 3.68553912426468e-10 27 0.99999999843926 3.12148166031589e-09 1.56074083015795e-09 28 0.999999999640903 7.18194955130118e-10 3.59097477565059e-10 29 0.999999999921718 1.56563171009302e-10 7.82815855046509e-11 30 0.99999999964679 7.06419283817127e-10 3.53209641908564e-10 31 0.999999998491513 3.01697368991477e-09 1.50848684495739e-09 32 0.99999999014443 1.97111400926475e-08 9.85557004632377e-09 33 0.999999974618775 5.07624498408896e-08 2.53812249204448e-08 34 0.999999856353748 2.87292503126202e-07 1.43646251563101e-07 35 0.999999009858187 1.98028362498962e-06 9.9014181249481e-07 36 0.999994659329696 1.06813406085621e-05 5.34067030428106e-06 37 0.999991956191167 1.60876176657871e-05 8.04380883289354e-06 38 0.999993811715211 1.23765695774905e-05 6.18828478874526e-06 39 0.999960094048658 7.9811902684315e-05 3.99059513421575e-05 40 0.99989513382035 0.00020973235929899 0.000104866179649495 41 0.999808944851918 0.0003821102961638 0.0001910551480819 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 34 1 NOK 5% type I error level 34 1 NOK 10% type I error level 34 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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