*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, 10 Dec 2010 10:44:38 +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/10/t1291977824h1y3g1wxainwxq0.htm/, Retrieved Fri, 10 Dec 2010 11:43:54 +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/10/t1291977824h1y3g1wxainwxq0.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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101.82 107.34 93.63 99.85 101.76 101.68 107.34 93.63 99.91 102.37 101.68 107.34 93.63 99.87 102.38 102.45 107.34 96.13 99.86 102.86 102.45 107.34 96.13 100.10 102.87 102.45 107.34 96.13 100.10 102.92 102.45 107.34 96.13 100.12 102.95 102.45 107.34 96.13 99.95 103.02 102.45 112.60 96.13 99.94 104.08 102.52 112.60 96.13 100.18 104.16 102.52 112.60 96.13 100.31 104.24 102.85 112.60 96.13 100.65 104.33 102.85 112.61 96.13 100.65 104.73 102.85 112.61 96.13 100.69 104.86 103.25 112.61 96.13 101.26 105.03 103.25 112.61 98.73 101.26 105.62 103.25 112.61 98.73 101.38 105.63 103.25 112.61 98.73 101.38 105.63 104.45 112.61 98.73 101.38 105.94 104.45 112.61 98.73 101.44 106.61 104.45 118.65 98.73 101.40 107.69 104.80 118.65 98.73 101.40 107.78 104.80 118.65 98.73 100.58 107.93 105.29 118.65 98.73 100.58 108.48 105.29 114.29 98.73 100.58 108.14 105.29 114.29 98.73 100.59 108.48 105.29 114.29 98.73 100.81 108.48 106.04 114.29 101.67 100.75 108.89 105.94 114.29 101.67 100.75 108.93 105.94 114.29 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation bios[t] = -174.117057776151 -0.222841174760951schouwburg[t] -0.0355988545204506eedagsacttractie[t] + 1.94413794987770huurDVD[t] + 1.04536917079398vrijetijdsbesteding[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) -174.117057776151 42.558301 -4.0913 0.000147 7.3e-05 schouwburg -0.222841174760951 0.171312 -1.3008 0.198956 0.099478 eedagsacttractie -0.0355988545204506 0.23151 -0.1538 0.878377 0.439188 huurDVD 1.94413794987770 0.514586 3.7781 0.000402 0.000201 vrijetijdsbesteding 1.04536917079398 0.383945 2.7227 0.008746 0.004373 Multiple Linear Regression - Regression Statistics Multiple R 0.958447028955653 R-squared 0.918620707313919 Adjusted R-squared 0.91247887390365 F-TEST (value) 149.567831940512 F-TEST (DF numerator) 4 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.93511710571985 Sum Squared Residuals 198.467945281026 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.82 99.1289908915415 2.69100910845848 2 101.68 99.8833143627193 1.79668563728074 3 101.68 99.8160025364321 1.86399746356790 4 102.45 100.209341222613 2.2406587773867 5 102.45 100.686388022292 1.76361197770811 6 102.45 100.738656480832 1.71134351916842 7 102.45 100.808900314953 1.64109968504703 8 102.45 100.551572705429 1.89842729457067 9 102.45 100.468078067730 1.98192193227043 10 102.52 101.018300709364 1.50169929063624 11 102.52 101.354668176511 1.16533182348863 12 102.85 102.109758304841 0.740241695158742 13 102.85 102.525677561411 0.324322438588753 14 102.85 102.739341071610 0.110658928390447 15 103.25 104.025212462075 -0.775212462074827 16 103.25 104.54942325109 -1.29942325109011 17 103.25 104.793173496783 -1.54317349678334 18 103.25 104.793173496783 -1.54317349678334 19 104.45 105.117237939729 -0.667237939729479 20 104.45 105.934283561154 -1.48428356115412 21 104.45 105.639556052060 -1.18955605206038 22 104.8 105.733639277432 -0.933639277431848 23 104.8 104.296251534151 0.503748465848773 24 105.29 104.871204578088 0.418795421912094 25 105.29 105.487366581976 -0.197366581975693 26 105.29 105.862233479544 -0.572233479544439 27 105.29 106.289943828518 -0.99994382851753 28 106.04 106.497236279260 -0.457236279260268 29 105.94 106.539051046092 -0.599051046092042 30 105.94 107.240023383389 -1.30002338338865 31 105.94 108.192267650252 -2.2522676502523 32 106.28 109.178805000074 -2.89880500007395 33 106.48 108.831938448889 -2.35193844888935 34 107.19 109.482299995852 -2.29229999585162 35 108.14 109.764549671966 -1.624549671966 36 108.22 109.620938331601 -1.40093833160082 37 108.22 109.894583648501 -1.67458364850079 38 108.61 110.358944095401 -1.74894409540145 39 108.61 110.786462780086 -2.17646278008633 40 108.61 111.232294231551 -2.62229423155125 41 108.61 111.404142974918 -2.79414297491784 42 109.06 112.449512145712 -3.38951214571182 43 109.06 113.186818562748 -4.12681856274822 44 112.93 113.926290330466 -0.996290330465953 45 115.84 116.624235092372 -0.784235092371702 46 118.57 118.152384370809 0.417615629191276 47 118.57 117.956696236192 0.613303763807938 48 118.86 118.137532667349 0.722467332650521 49 118.98 118.158440050765 0.82155994923465 50 119.27 118.522853256626 0.74714674337387 51 119.39 116.161458649483 3.22854135051672 52 119.49 116.811053104864 2.67894689513566 53 119.59 116.815451116616 2.77454888338433 54 120.12 117.230666777099 2.88933322290095 55 120.14 117.483021382007 2.65697861799329 56 120.14 117.602218338257 2.53778166174286 57 120.14 117.743377395894 2.39662260410551 58 120.14 118.282763017244 1.85723698275573 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 1.13598124113785e-06 2.27196248227571e-06 0.999998864018759 9 9.7025212824279e-09 1.94050425648558e-08 0.999999990297479 10 2.52824073213857e-09 5.05648146427715e-09 0.99999999747176 11 5.54012850145514e-11 1.10802570029103e-10 0.9999999999446 12 1.59918093481165e-09 3.19836186962331e-09 0.99999999840082 13 2.97258277185938e-10 5.94516554371876e-10 0.999999999702742 14 1.93145792500399e-11 3.86291585000797e-11 0.999999999980685 15 1.38598836815930e-12 2.77197673631861e-12 0.999999999998614 16 2.49644826937587e-10 4.99289653875175e-10 0.999999999750355 17 1.21167577926635e-10 2.42335155853271e-10 0.999999999878832 18 2.39715237498871e-11 4.79430474997741e-11 0.999999999976029 19 6.10354653733489e-09 1.22070930746698e-08 0.999999993896453 20 1.55240657835622e-09 3.10481315671244e-09 0.999999998447593 21 3.87622631679294e-10 7.75245263358588e-10 0.999999999612377 22 2.05100380557893e-10 4.10200761115786e-10 0.9999999997949 23 1.68989075731191e-10 3.37978151462382e-10 0.99999999983101 24 2.46514572704650e-10 4.93029145409301e-10 0.999999999753485 25 1.30323316801563e-10 2.60646633603125e-10 0.999999999869677 26 5.8593958269158e-11 1.17187916538316e-10 0.999999999941406 27 1.53441913446854e-11 3.06883826893707e-11 0.999999999984656 28 1.25077354724220e-11 2.50154709448441e-11 0.999999999987492 29 1.90926202867996e-11 3.81852405735993e-11 0.999999999980907 30 2.16696546353056e-11 4.33393092706112e-11 0.99999999997833 31 1.41703728469706e-11 2.83407456939411e-11 0.99999999998583 32 5.51593918059057e-12 1.10318783611811e-11 0.999999999994484 33 2.45292467131246e-12 4.90584934262492e-12 0.999999999997547 34 1.26589138451746e-12 2.53178276903491e-12 0.999999999998734 35 9.015429546489e-11 1.80308590929780e-10 0.999999999909846 36 8.1674834475244e-10 1.63349668950488e-09 0.999999999183252 37 2.70869271842375e-09 5.4173854368475e-09 0.999999997291307 38 4.07929231129996e-09 8.15858462259992e-09 0.999999995920708 39 1.19246499472185e-08 2.38492998944371e-08 0.99999998807535 40 5.98593285585271e-09 1.19718657117054e-08 0.999999994014067 41 4.09608423020220e-09 8.19216846040439e-09 0.999999995903916 42 1.80530425354315e-09 3.61060850708631e-09 0.999999998194696 43 4.64181317624015e-07 9.28362635248031e-07 0.999999535818682 44 0.225556161495110 0.451112322990219 0.77444383850489 45 0.999933456590562 0.000133086818876887 6.65434094384437e-05 46 0.999984652596758 3.06948064850012e-05 1.53474032425006e-05 47 0.999986263947679 2.74721046426459e-05 1.37360523213230e-05 48 0.999929472802998 0.000141054394003494 7.05271970017472e-05 49 0.999478207472525 0.00104358505494942 0.00052179252747471 50 0.995907631262439 0.00818473747512257 0.00409236873756129 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 42 0.976744186046512 NOK 5% type I error level 42 0.976744186046512 NOK 10% type I error level 42 0.976744186046512 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = quantiles ; par3 = 2 ; par4 = no ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

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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