*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: Sun, 13 Dec 2009 06:15:19 -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/13/t1260710172k9u9rn06ibt2wmn.htm/, Retrieved Sun, 13 Dec 2009 14:16:46 +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/13/t1260710172k9u9rn06ibt2wmn.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:

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507 104.5 501 509 510 517 519 569 87.4 507 501 509 510 517 580 89.9 569 507 501 509 510 578 109.8 580 569 507 501 509 565 111.7 578 580 569 507 501 547 98.6 565 578 580 569 507 555 96.9 547 565 578 580 569 562 95.1 555 547 565 578 580 561 97 562 555 547 565 578 555 112.7 561 562 555 547 565 544 102.9 555 561 562 555 547 537 97.4 544 555 561 562 555 543 111.4 537 544 555 561 562 594 87.4 543 537 544 555 561 611 96.8 594 543 537 544 555 613 114.1 611 594 543 537 544 611 110.3 613 611 594 543 537 594 103.9 611 613 611 594 543 595 101.6 594 611 613 611 594 591 94.6 595 594 611 613 611 589 95.9 591 595 594 611 613 584 104.7 589 591 595 594 611 573 102.8 584 589 591 595 594 567 98.1 573 584 589 591 595 569 113.9 567 573 584 589 591 621 80.9 569 567 573 584 589 629 95.7 621 569 567 573 584 628 113.2 629 621 569 567 573 612 105.9 628 629 621 569 567 595 108.8 612 628 629 621 569 597 102.3 595 612 628 629 621 593 99 597 595 612 628 629 590 100.7 593 597 595 612 628 580 115.5 590 593 59 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 243.301929501305 -1.54574360309231X[t] + 0.889239136592848`Yt-1`[t] + 0.0310888319576515`Yt-2`[t] + 0.0174977223073751`Yt-3`[t] -0.347038931375699`Yt-4`[t] + 0.266291251496857`Yt-5`[t] -0.0304035045744285t + 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) 243.301929501305 35.203991 6.9112 0 0 X -1.54574360309231 0.228481 -6.7653 0 0 `Yt-1` 0.889239136592848 0.099542 8.9333 0 0 `Yt-2` 0.0310888319576515 0.162016 0.1919 0.848489 0.424245 `Yt-3` 0.0174977223073751 0.150517 0.1163 0.907848 0.453924 `Yt-4` -0.347038931375699 0.147972 -2.3453 0.022394 0.011197 `Yt-5` 0.266291251496857 0.091754 2.9022 0.005202 0.002601 t -0.0304035045744285 0.100142 -0.3036 0.762499 0.381249 Multiple Linear Regression - Regression Statistics Multiple R 0.955334021847317 R-squared 0.91266309329897 Adjusted R-squared 0.902301087419188 F-TEST (value) 88.077839743329 F-TEST (DF numerator) 7 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12.6291749440012 Sum Squared Residuals 9410.26752620514 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 507 510.784212755440 -3.78421275544049 2 569 544.151941321968 24.8480586780318 3 580 593.919556662604 -13.9195566626042 4 578 577.453000073742 0.54699992625841 5 565 569.921477784468 -4.92147778446847 6 547 558.79183774985 -11.7918377498499 7 555 557.636372999469 -2.63637299946930 8 562 570.338433337187 -8.33843333718706 9 561 577.508466201906 -16.508466201906 10 555 555.463167089655 -0.463167089655524 11 544 557.767457322074 -13.7674573220736 12 537 555.954039910277 -18.9540399102772 13 543 529.822666212736 13.1773337872642 14 594 573.631389569606 20.3686104303935 15 611 606.705921833945 4.29407816605457 16 613 596.241804834801 16.7581951651985 17 611 601.338326927387 9.66167307261248 18 594 593.680605161379 0.319394838620695 19 595 589.742356395491 5.25764360450893 20 591 604.690765073956 -13.6907650739560 21 589 600.054226257468 -11.0542262574675 22 584 589.903022497365 -5.90302249736505 23 573 583.357177395735 -10.3571773957347 24 567 582.27414569577 -15.2741456957694 25 569 551.685005536472 17.3149944635276 26 621 605.266223423887 15.7337765761125 27 629 631.042413014094 -2.04241301409448 28 628 611.880054076349 16.1199459236511 29 612 621.111106581668 -9.11110658166762 30 595 584.965671460599 10.0343285394013 31 597 590.421450647247 6.57854935275301 32 593 598.939374549215 -5.93937454921535 33 590 597.775298408217 -7.77529840821684 34 580 573.749814094319 6.25018590568094 35 574 582.319738026282 -8.31973802628186 36 573 564.290415295699 8.709584704301 37 573 555.720219293318 17.2797807066821 38 620 603.360969392503 16.6390306074967 39 626 621.185900252077 4.81409974792284 40 620 604.597264567244 15.4027354327560 41 588 597.346296806551 -9.34629680655128 42 566 558.032541469579 7.9674585304215 43 557 564.621108509276 -7.62110850927655 44 561 552.840678043328 8.15932195667174 45 549 566.29200052395 -17.2920005239500 46 532 533.803601007945 -1.80360100794540 47 526 535.248943695753 -9.24894369575297 48 511 520.413466041783 -9.41346604178298 49 499 499.578738935411 -0.578738935411133 50 555 529.190180790318 25.8098192096819 51 565 557.791719273468 7.20828072653168 52 542 558.96287361275 -16.9628736127505 53 527 524.637967468772 2.36203253122816 54 510 502.165502616491 7.83449738350896 55 514 518.149564388598 -4.14956438859846 56 517 514.990492836027 2.00950716397332 57 508 513.28952440955 -5.28952440954997 58 493 511.961749930953 -18.9617499309533 59 490 480.857269032648 9.14273096735224 60 469 490.234481895381 -21.2344818953809 61 478 464.585491827717 13.4145081722828 62 528 505.422142323146 22.5778576768537 63 534 540.938965297302 -6.93896529730173 64 518 528.167220262763 -10.1672202627633 65 506 507.955260979404 -1.95526097940416 66 502 507.101848283329 -5.10184828332873 67 516 521.977080054333 -5.97708005433252 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.543857726186619 0.912284547626762 0.456142273813381 12 0.555126598611576 0.889746802776849 0.444873401388424 13 0.798717393139307 0.402565213721385 0.201282606860692 14 0.818806420866328 0.362387158267343 0.181193579133671 15 0.759677384496011 0.480645231007978 0.240322615503989 16 0.763887937742368 0.472224124515264 0.236112062257632 17 0.682954393581388 0.634091212837224 0.317045606418612 18 0.60927822859636 0.78144354280728 0.39072177140364 19 0.53282007057327 0.93435985885346 0.46717992942673 20 0.530820720544797 0.938358558910405 0.469179279455203 21 0.52637169993283 0.94725660013434 0.47362830006717 22 0.481314117698492 0.962628235396984 0.518685882301508 23 0.554481823478491 0.891036353043018 0.445518176521509 24 0.765554206213763 0.468891587572474 0.234445793786237 25 0.730820691597873 0.538358616804255 0.269179308402127 26 0.66679962654676 0.66640074690648 0.33320037345324 27 0.63873006082824 0.722539878343521 0.361269939171761 28 0.580959336364687 0.838081327270626 0.419040663635313 29 0.650513529748457 0.698972940503087 0.349486470251543 30 0.580035120614413 0.839929758771173 0.419964879385587 31 0.508824074838579 0.982351850322843 0.491175925161421 32 0.477281916367058 0.954563832734116 0.522718083632942 33 0.497450643754483 0.994901287508965 0.502549356245517 34 0.422552081035271 0.845104162070542 0.577447918964729 35 0.577260176347932 0.845479647304137 0.422739823652068 36 0.499859741198009 0.999719482396018 0.500140258801991 37 0.449802954126582 0.899605908253163 0.550197045873418 38 0.372507021680055 0.74501404336011 0.627492978319945 39 0.306004798622369 0.612009597244738 0.693995201377631 40 0.420063745427429 0.840127490854858 0.579936254572571 41 0.417519359062853 0.835038718125706 0.582480640937147 42 0.438400302193004 0.876800604386007 0.561599697806996 43 0.392783843041273 0.785567686082546 0.607216156958727 44 0.490610396505209 0.981220793010418 0.509389603494791 45 0.544874872666805 0.91025025466639 0.455125127333195 46 0.539987236205005 0.92002552758999 0.460012763794995 47 0.54538257224731 0.90923485550538 0.45461742775269 48 0.56008110519405 0.8798377896119 0.43991889480595 49 0.467955589667521 0.935911179335042 0.532044410332479 50 0.455620547611068 0.911241095222136 0.544379452388932 51 0.365429117466023 0.730858234932045 0.634570882533977 52 0.351879722674795 0.70375944534959 0.648120277325205 53 0.253192084706822 0.506384169413645 0.746807915293177 54 0.231227457516012 0.462454915032024 0.768772542483988 55 0.191806753299484 0.383613506598969 0.808193246700516 56 0.132570136502891 0.265140273005782 0.86742986349711 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 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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