ws7TimDamen

*Unverified author*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 28 Jan 2011 13:33:30 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/28/t1296221504twv37l2ic02wxjm.htm/, Retrieved Fri, 28 Jan 2011 14:31:44 +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/2011/Jan/28/t1296221504twv37l2ic02wxjm.htm/}, year = {2011}, } @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 = {2011}, 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 «

6654,00 5712,00 3,30 38,60 645,00 3,00 1,00 6,60 8,30 4,50 42,00 3,00 3,39 44,50 12,50 14,00 60,00 1,00 0,92 5,70 16,50 25,00 5,00 2547,00 4603,00 3,90 69,00 624,00 3,00 10,55 179,50 9,80 27,00 180,00 4,00 0,02 0,30 19,70 19,00 35,00 1,00 160,00 169,00 6,20 30,40 392,00 4,00 3,30 25,60 14,50 28,00 63,00 1,00 52,16 440,00 9,70 50,00 230,00 1,00 0,43 6,40 12,50 7,00 112,00 5,00 465,00 423,00 3,90 30,00 281,00 5,00 0,55 2,40 10,30 2,00 187,10 419,00 3,10 40,00 365,00 5,00 0,08 1,20 8,40 3,50 42,00 1,00 3,00 25,00 8,60 50,00 28,00 2,00 0,79 3,50 10,70 6,00 42,00 2,00 0,20 5,00 10,70 10,40 120,00 2,00 1,41 17,50 6,10 34,00 1,00 60,00 81,00 18,10 7,00 1,00 529,00 680,00 28,00 400,00 5,00 27,66 115,00 3,80 20,00 148,00 5,00 0,12 1,00 14,40 3,90 16,00 3,00 207,00 406,00 12,00 39,30 252,00 1,00 85,00 325,00 6,20 41,00 310,00 1,00 36,33 119,50 13,00 16,20 63,00 1,00 0,10 4,00 13,80 9,00 28,00 5,00 1,04 5,50 8,20 7,60 68,00 5,00 521,00 655,00 2,90 46,00 336,00 5,00 100,00 157,00 10,80 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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 Y[t] = + 10.1204183249928 -0.0120503930556895G[t] -0.0130609895244657H[t] + 0.119711702613191J[t] + 0.245246671582954Z[t] + 0.000989834348735287P[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) 10.1204183249928 14.745474 0.6863 0.49533 0.247665 G -0.0120503930556895 0.028689 -0.42 0.676071 0.338036 H -0.0130609895244657 0.042102 -0.3102 0.757545 0.378773 J 0.119711702613191 0.158877 0.7535 0.454315 0.227157 Z 0.245246671582954 0.122129 2.0081 0.049467 0.024733 P 0.000989834348735287 0.034605 0.0286 0.977282 0.488641 Multiple Linear Regression - Regression Statistics Multiple R 0.326715892536400 R-squared 0.106743274435857 Adjusted R-squared 0.0269882096533440 F-TEST (value) 1.33838866192309 F-TEST (DF numerator) 5 F-TEST (DF denominator) 56 p-value 0.261640216229769 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 88.054285716776 Sum Squared Residuals 434199.205053131 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.3 18.1406751636078 -14.8406751636078 2 8.3 20.8641977723653 -12.5641977723653 3 12.5 25.8901074246059 -13.3901074246059 4 16.5 16.7750183325654 -0.275018332565432 5 69 30.0478064282679 38.9521935717321 6 27 30.3584880275500 -3.35848802754995 7 19 14.4530314722864 4.54696852771358 8 30.4 55.9141643275831 -25.5141643275831 9 28 17.4612576105064 10.5387423894936 10 50 32.4709176834889 17.5290823165110 11 7 24.9742504631347 -17.9742504631347 12 30 39.837930404404 -9.83793040440398 13 2 135.116452628224 -133.116452628224 14 5 5.18332897697325 -0.183328976973246 15 1 16.0284948620829 -15.0284948620829 16 2 10.1157177886595 -8.11571778865953 17 2 10.7603213326 -8.7603213326 18 2 12.8944237371913 -10.8944237371913 19 60 23.840185479336 36.159814520664 20 680 104.654649951589 575.34535004841 21 3.8 46.9807812760436 -43.1807812760436 22 14.4 14.4997031768666 -0.0997031768665824 23 12 68.8310462014836 -56.8310462014836 24 6.2 85.7869511520132 -79.5869511520132 25 13 25.5126990235145 -12.5126990235145 26 13.8 18.0162306271745 -4.21623062717449 27 8.2 27.6275822530751 -19.4275822530751 28 2.9 83.2017845482766 -80.3017845482766 29 10.8 34.0720027952624 -23.2720027952624 30 16.3 13.6534752540013 2.64652474599874 31 2.6 13.7999211277342 -11.1999211277342 32 24 16.1496935670561 7.85030643294388 33 100 26.3178016247137 73.6821983752863 34 30 10.5243447269545 19.4756552730455 35 3 9.51126811025689 -6.51126811025689 36 4 9.9332851326666 -5.93328513266661 37 4 11.4722545649280 -7.47225456492796 38 2 12.9883126153308 -10.9883126153308 39 2 158.596926846770 -156.596926846770 40 0.48 10.7895432524666 -10.3095432524666 41 10 24.8672704927630 -14.8672704927630 42 1.62 12.7570682044381 -11.1370682044381 43 192 33.5243437030842 158.475656296916 44 2.5 12.2087798266843 -9.70877982668432 45 4.29 17.4533940604458 -13.1633940604458 46 0.28 12.8044821047346 -12.5244821047346 47 4.24 18.2747646720853 -14.0347646720853 48 6.8 33.2922049076434 -26.4922049076434 49 0.75 11.2160426998417 -10.4660426998417 50 3.6 11.2271746959311 -7.62717469593112 51 14.83 19.7800546455488 -4.95005464554882 52 55.5 30.1488364153154 25.3511635846846 53 1.4 12.4421845922677 -11.0421845922677 54 0.06 11.6589778110700 -11.5989778110700 55 2.6 12.8276779830566 -10.2276779830566 56 12.3 12.7539556605630 -0.453955660562951 57 2.5 12.5840056728443 -10.0840056728443 58 58 17.3563574678594 40.6436425321406 59 3.9 13.0985080157615 -9.19850801576149 60 17 20.9220156884773 -3.92201568847729 61 3.3 18.1406751636078 -14.8406751636078 62 8.3 20.8641977723653 -12.5641977723653 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.000160336155675089 0.000320672311350177 0.999839663844325 10 0.00022248001421323 0.00044496002842646 0.999777519985787 11 7.99151160019593e-05 0.000159830232003919 0.999920084883998 12 8.44196857805806e-06 1.68839371561161e-05 0.999991558031422 13 1.40727334770573e-06 2.81454669541147e-06 0.999998592726652 14 2.31487646231095e-07 4.62975292462189e-07 0.999999768512354 15 4.2147455410618e-08 8.4294910821236e-08 0.999999957852545 16 6.4050421309236e-09 1.28100842618472e-08 0.999999993594958 17 8.3819728849268e-10 1.67639457698536e-09 0.999999999161803 18 9.78181548896698e-11 1.95636309779340e-10 0.999999999902182 19 4.2468584887981e-09 8.4937169775962e-09 0.999999995753141 20 0.999999999999995 9.26654733059169e-15 4.63327366529585e-15 21 0.999999999999988 2.47278857144052e-14 1.23639428572026e-14 22 0.99999999999994 1.21299238416744e-13 6.0649619208372e-14 23 0.9999999999999 2.01615437212864e-13 1.00807718606432e-13 24 0.999999999999886 2.29001437464186e-13 1.14500718732093e-13 25 0.99999999999947 1.05939286752355e-12 5.29696433761775e-13 26 0.999999999997638 4.72323329484307e-12 2.36161664742153e-12 27 0.999999999990501 1.89978294405391e-11 9.49891472026956e-12 28 0.999999999985583 2.88336352562653e-11 1.44168176281327e-11 29 0.999999999946926 1.06148335675553e-10 5.30741678377764e-11 30 0.999999999771467 4.57066256754119e-10 2.28533128377059e-10 31 0.999999999057708 1.88458329152106e-09 9.42291645760532e-10 32 0.999999996326044 7.3479127510349e-09 3.67395637551745e-09 33 0.999999991458285 1.70834302136221e-08 8.54171510681105e-09 34 0.999999975543737 4.89125259417864e-08 2.44562629708932e-08 35 0.99999990984157 1.80316860999706e-07 9.01584304998531e-08 36 0.999999678788439 6.42423122309911e-07 3.21211561154955e-07 37 0.999998903838847 2.19232230661293e-06 1.09616115330647e-06 38 0.999996411437892 7.17712421688893e-06 3.58856210844447e-06 39 0.999996184553976 7.63089204846793e-06 3.81544602423397e-06 40 0.999989086167063 2.18276658743064e-05 1.09138329371532e-05 41 0.999976569036477 4.68619270452844e-05 2.34309635226422e-05 42 0.999929088723335 0.000141822553329095 7.09112766645475e-05 43 0.999999999861562 2.76876847352376e-10 1.38438423676188e-10 44 0.999999998768155 2.46368995675849e-09 1.23184497837924e-09 45 0.99999998959382 2.08123586073642e-08 1.04061793036821e-08 46 0.999999916751143 1.66497714071765e-07 8.32488570358824e-08 47 0.99999937035813 1.25928374080833e-06 6.29641870404163e-07 48 0.999999888268832 2.23462335916333e-07 1.11731167958166e-07 49 0.999998867864728 2.26427054480413e-06 1.13213527240206e-06 50 0.999990437390183 1.91252196339293e-05 9.56260981696467e-06 51 0.999940229013657 0.000119541972686882 5.97709863434412e-05 52 0.999619468326631 0.000761063346737145 0.000380531673368572 53 0.999535310496333 0.000929379007333708 0.000464689503666854 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 45 1 NOK 5% type I error level 45 1 NOK 10% type I error level 45 1 NOK

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 = 3 ; 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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