*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: Sat, 12 Dec 2009 07:10:13 -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/Dec/12/t1260627121gs7sbr6s1a41njn.htm/, Retrieved Sat, 12 Dec 2009 15:12:13 +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/Dec/12/t1260627121gs7sbr6s1a41njn.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 «

467 98.8 460 100.5 448 110.4 443 96.4 436 101.9 431 106.2 484 81 510 94.7 513 101 503 109.4 471 102.3 471 90.7 476 96.2 475 96.1 470 106 461 103.1 455 102 456 104.7 517 86 525 92.1 523 106.9 519 112.6 509 101.7 512 92 519 97.4 517 97 510 105.4 509 102.7 501 98.1 507 104.5 569 87.4 580 89.9 578 109.8 565 111.7 547 98.6 555 96.9 562 95.1 561 97 555 112.7 544 102.9 537 97.4 543 111.4 594 87.4 611 96.8 613 114.1 611 110.3 594 103.9 595 101.6 591 94.6 589 95.9 584 104.7 573 102.8 567 98.1 569 113.9 621 80.9 629 95.7 628 113.2 612 105.9 595 108.8 597 102.3 593 99 590 100.7 580 115.5 574 100.7 573 109.9 573 114.6 620 85.4 626 100.5 620 114.8 588 116.5 566 112.9 557 102

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] = + 482.709293482212 + 0.597911770962894X[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) 482.709293482212 79.994555 6.0343 0 0 X 0.597911770962894 0.785063 0.7616 0.448851 0.224426 Multiple Linear Regression - Regression Statistics Multiple R 0.0906549585695 R-squared 0.00821832151323775 Adjusted R-squared -0.00594998817943027 F-TEST (value) 0.580049539536156 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.448851281961188 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 55.4158779872254 Sum Squared Residuals 214964.367316654 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 467 541.782976453349 -74.7829764533488 2 460 542.799426463984 -82.7994264639836 3 448 548.718752996516 -100.718752996516 4 443 540.347988203036 -97.3479882030357 5 436 543.636502943332 -107.636502943332 6 431 546.207523558472 -115.207523558472 7 484 531.140146930207 -47.1401469302072 8 510 539.331538192399 -29.3315381923988 9 513 543.098382349465 -30.0983823494650 10 503 548.120841225553 -45.1208412255533 11 471 543.875667651717 -72.8756676517168 12 471 536.939891108547 -65.9398911085472 13 476 540.228405848843 -64.2284058488431 14 475 540.168614671747 -65.1686146717469 15 470 546.08794120428 -76.0879412042795 16 461 544.353997068487 -83.3539970684871 17 455 543.696294120428 -88.696294120428 18 456 545.310655902028 -89.3106559020277 19 517 534.129705785022 -17.1297057850216 20 525 537.776967587895 -12.7769675878953 21 523 546.626061798146 -23.6260617981461 22 519 550.034158892635 -31.0341588926346 23 509 543.516920589139 -34.5169205891391 24 512 537.717176410799 -25.717176410799 25 519 540.945899973999 -21.9458999739986 26 517 540.706735265613 -23.7067352656135 27 510 545.729194141702 -35.7291941417018 28 509 544.114832360102 -35.1148323601019 29 501 541.364438213673 -40.3644382136726 30 507 545.191073547835 -38.1910735478352 31 569 534.96678226437 34.0332177356303 32 580 536.461561691777 43.5384383082231 33 578 548.360005933939 29.6399940660615 34 565 549.496038298768 15.503961701232 35 547 541.663394099154 5.33660590084592 36 555 540.646944088517 14.3530559114828 37 562 539.570702900784 22.4292970992161 38 561 540.706735265613 20.2932647343865 39 555 550.093950069731 4.90604993026912 40 544 544.234414714295 -0.234414714294529 41 537 540.945899973999 -3.94589997399861 42 543 549.316664767479 -6.31666476747913 43 594 534.96678226437 59.0332177356303 44 611 540.587152911421 70.4128470885791 45 613 550.931026549079 62.0689734509211 46 611 548.65896181942 62.3410381805801 47 594 544.832326485257 49.1676735147426 48 595 543.457129412043 51.5428705879572 49 591 539.271747015302 51.7282529846975 50 589 540.049032317554 48.9509676824457 51 584 545.310655902028 38.6893440979723 52 573 544.174623537198 28.8253764628018 53 567 541.364438213673 25.6355617863274 54 569 550.811444194886 18.1885558051136 55 621 531.080355753111 89.9196442468891 56 629 539.929449963362 89.0705500366383 57 628 550.392905955212 77.6070940447877 58 612 546.028150027183 65.9718499728168 59 595 547.762094162976 47.2379058370244 60 597 543.875667651717 53.1243323482832 61 593 541.902558807539 51.0974411924608 62 590 542.919008818176 47.0809911818238 63 580 551.768103028427 28.231896971573 64 574 542.919008818176 31.0809911818238 65 573 548.419797111035 24.5802028889652 66 573 551.22998243456 21.7700175654396 67 620 533.770958722444 86.2290412775561 68 626 542.799426463984 83.2005735360164 69 620 551.349564788753 68.650435211247 70 588 552.36601479939 35.6339852006101 71 566 550.213532423923 15.7864675760765 72 557 543.696294120428 13.3037058795721 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0291564972826792 0.0583129945653584 0.97084350271732 6 0.0144732623483473 0.0289465246966945 0.985526737651653 7 0.00446432297962728 0.00892864595925455 0.995535677020373 8 0.0286455242169029 0.0572910484338058 0.971354475783097 9 0.0751747949328257 0.150349589865651 0.924825205067174 10 0.102021185681162 0.204042371362323 0.897978814318838 11 0.06838951128875 0.1367790225775 0.93161048871125 12 0.0458020185371925 0.091604037074385 0.954197981462807 13 0.0305063017722748 0.0610126035445496 0.969493698227725 14 0.0208659361884329 0.0417318723768657 0.979134063811567 15 0.0156339254595871 0.0312678509191742 0.984366074540413 16 0.0137627567578654 0.0275255135157309 0.986237243242135 17 0.0157202602776343 0.0314405205552686 0.984279739722366 18 0.0204373225228460 0.0408746450456920 0.979562677477154 19 0.0248303481374608 0.0496606962749217 0.97516965186254 20 0.040488483943726 0.080976967887452 0.959511516056274 21 0.104572242726814 0.209144485453628 0.895427757273186 22 0.180859054305167 0.361718108610335 0.819140945694833 23 0.211891435469727 0.423782870939455 0.788108564530273 24 0.235741289761998 0.471482579523996 0.764258710238002 25 0.281508001310976 0.563016002621953 0.718491998689024 26 0.332520658977468 0.665041317954937 0.667479341022532 27 0.411803191166727 0.823606382333455 0.588196808833273 28 0.509613976688734 0.980772046622532 0.490386023311266 29 0.660719771677785 0.67856045664443 0.339280228322215 30 0.812170337763578 0.375659324472843 0.187829662236422 31 0.90022590384946 0.199548192301081 0.0997740961505404 32 0.949436861565674 0.101126276868652 0.050563138434326 33 0.985071939450042 0.0298561210999166 0.0149280605499583 34 0.99177460870239 0.0164507825952198 0.00822539129760988 35 0.99448090488398 0.01103819023204 0.00551909511602 36 0.996080815784387 0.00783836843122677 0.00391918421561339 37 0.997046761464822 0.00590647707035634 0.00295323853517817 38 0.997761508868407 0.00447698226318688 0.00223849113159344 39 0.998261472362198 0.00347705527560352 0.00173852763780176 40 0.999077046188345 0.00184590762330924 0.000922953811654622 41 0.999789955976921 0.000420088046158435 0.000210044023079217 42 0.999926727785333 0.000146544429334513 7.32722146672565e-05 43 0.9999356009522 0.000128798095601847 6.43990478009235e-05 44 0.999958764470687 8.24710586254401e-05 4.12355293127201e-05 45 0.999983371574183 3.32568516346054e-05 1.66284258173027e-05 46 0.99998918828546 2.16234290818674e-05 1.08117145409337e-05 47 0.999983454408147 3.30911837062954e-05 1.65455918531477e-05 48 0.999973579427061 5.28411458776876e-05 2.64205729388438e-05 49 0.999957286005275 8.54279894499194e-05 4.27139947249597e-05 50 0.999928497220863 0.000143005558273435 7.15027791367177e-05 51 0.999868665433233 0.000262669133534290 0.000131334566767145 52 0.999807011407633 0.000385977184734665 0.000192988592367332 53 0.99982499058817 0.000350018823658667 0.000175009411829333 54 0.99969733583125 0.00060532833749998 0.00030266416874999 55 0.999504833717833 0.00099033256433431 0.000495166282167155 56 0.999529260293 0.000941479413998706 0.000470739706999353 57 0.999802119393915 0.000395761212170312 0.000197880606085156 58 0.999714386877604 0.000571226244791038 0.000285613122395519 59 0.999316056504416 0.00136788699116811 0.000683943495584055 60 0.998334758727316 0.00333048254536816 0.00166524127268408 61 0.995922979634152 0.00815404073169596 0.00407702036584798 62 0.990348434895232 0.0193031302095352 0.0096515651047676 63 0.97748624252586 0.0450275149482811 0.0225137574741405 64 0.960580180441521 0.0788396391169574 0.0394198195584787 65 0.92335232533664 0.153295349326721 0.0766476746633605 66 0.852399083845043 0.295201832309914 0.147600916154957 67 0.741425430397605 0.51714913920479 0.258574569602395 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.428571428571429 NOK 5% type I error level 39 0.619047619047619 NOK 10% type I error level 45 0.714285714285714 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 1 ; 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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