*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, 20 Nov 2009 06:18:20 -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/Nov/20/t1258723147mgv6n0byyf2z582.htm/, Retrieved Fri, 20 Nov 2009 14:19:19 +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/Nov/20/t1258723147mgv6n0byyf2z582.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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501 98.1 509 510 517 519 507 104.5 501 509 510 517 569 87.4 507 501 509 510 580 89.9 569 507 501 509 578 109.8 580 569 507 501 565 111.7 578 580 569 507 547 98.6 565 578 580 569 555 96.9 547 565 578 580 562 95.1 555 547 565 578 561 97 562 555 547 565 555 112.7 561 562 555 547 544 102.9 555 561 562 555 537 97.4 544 555 561 562 543 111.4 537 544 555 561 594 87.4 543 537 544 555 611 96.8 594 543 537 544 613 114.1 611 594 543 537 611 110.3 613 611 594 543 594 103.9 611 613 611 594 595 101.6 594 611 613 611 591 94.6 595 594 611 613 589 95.9 591 595 594 611 584 104.7 589 591 595 594 573 102.8 584 589 591 595 567 98.1 573 584 589 591 569 113.9 567 573 584 589 621 80.9 569 567 573 584 629 95.7 621 569 567 573 628 113.2 629 621 569 567 612 105.9 628 629 621 569 595 108.8 612 628 629 621 597 102.3 595 612 628 629 593 99 597 595 612 628 590 100.7 593 597 595 612 580 115.5 590 593 597 595 574 100.7 580 590 593 597 573 109.9 574 580 590 593 573 114.6 573 574 580 590 620 85.4 573 573 5 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 233.322207177395 -1.47716393306426X[t] + 0.958869379347753`Yt-1`[t] + 0.0185945754162885`Yt-2`[t] -0.111140032855127`Yt-3`[t] -0.00830507336071676`Yt-4`[t] + 0.0238808955022916t + 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) 233.322207177395 37.136966 6.2827 0 0 X -1.47716393306426 0.245121 -6.0263 0 0 `Yt-1` 0.958869379347753 0.105429 9.0949 0 0 `Yt-2` 0.0185945754162885 0.174982 0.1063 0.91572 0.45786 `Yt-3` -0.111140032855127 0.156051 -0.7122 0.479054 0.239527 `Yt-4` -0.00830507336071676 0.100585 -0.0826 0.934466 0.467233 t 0.0238808955022916 0.103753 0.2302 0.81873 0.409365 Multiple Linear Regression - Regression Statistics Multiple R 0.947449405751214 R-squared 0.897660376458328 Adjusted R-squared 0.88759418397882 F-TEST (value) 89.1757611714314 F-TEST (DF numerator) 6 F-TEST (DF denominator) 61 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.6536518406792 Sum Squared Residuals 11371.7547237755 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 501 524.214323729296 -23.2143237292961 2 507 507.889396219694 -0.88939621969418 3 569 538.946515589732 30.0534844102683 4 580 595.736380960834 -15.7363809608336 5 578 577.464726826747 0.535273173252837 6 565 566.028285343129 -1.02828534312885 7 547 571.163067769649 -24.1630677696488 8 555 556.327673301431 -1.32767330143136 9 562 567.808132527576 -5.80813252757626 10 561 573.994730754103 -12.9947307541026 11 555 549.258801606714 5.74119839328586 12 544 557.142657377872 -13.1426573778718 13 537 554.684813799235 -17.6848137992346 14 543 527.786918917315 15.2130810826847 15 594 570.158159256103 23.8418407438969 16 611 606.179941016988 4.8200589830118 17 613 597.289283982015 15.7107160179845 18 611 599.442262248159 11.5577377518414 19 594 604.726503407476 -10.7265034074755 20 595 591.446426436439 3.55357356356116 21 591 602.658886379651 -11.6588863796506 22 589 598.851561925453 -9.85156192545325 23 584 583.914329363906 0.0856706360935728 24 573 582.349540742719 -9.34954074271928 25 567 578.93105643287 -11.93105643287 26 569 550.230300891288 18.7696991087117 27 621 602.070828612319 18.929171387681 28 629 630.889276179485 -1.88927617948462 29 628 613.528211577245 14.4717884227546 30 612 617.729384552911 -5.7293845529113 31 595 596.788001319949 -1.78800131994861 32 597 589.859854570766 7.14014542923441 33 593 598.146553021041 -5.14655302104129 34 590 593.883228596085 -3.88322859608452 35 580 569.013003023949 10.9869969760507 36 574 581.682382593775 -7.68238259377531 37 573 562.543833666845 10.4561663331548 38 573 555.690922793733 17.3090772062666 39 620 599.579286890034 20.4207131099662 40 626 622.525823698630 3.47417630137042 41 620 608.061726745326 11.9382732546743 42 588 594.709198586839 -6.709198586839 43 566 568.198303404662 -2.19830340466233 44 557 563.25012816856 -6.25012816855976 45 561 551.932759750045 9.06724024995476 46 549 559.369624807693 -10.3696248076927 47 532 529.202710265951 2.79728973404856 48 526 531.092844286289 -5.09284428628856 49 511 521.620936638641 -10.6209366386404 50 499 497.469655759087 1.53034424091322 51 555 523.002161062122 31.9978389378780 52 565 560.933705212242 4.06629478775771 53 542 560.785371974773 -18.7853719747732 54 527 518.193099002545 8.80690099745471 55 510 515.27197132739 -5.27197132739004 56 514 520.835604474552 -6.83560447455165 57 517 510.431318201704 6.56868179829617 58 508 512.318097936428 -4.3180979364275 59 493 507.896056058953 -14.8960560589533 60 490 481.924175195503 8.07582480449747 61 469 491.880618648458 -22.8806186484582 62 478 463.409590259645 14.5904097403549 63 528 501.52636795249 26.4736320475099 64 534 546.406701958522 -12.4067019585223 65 518 527.175887283712 -9.17588728371198 66 506 507.962558585516 -1.96255858551582 67 502 519.178171965965 -17.1781719659653 68 516 524.405386583227 -8.40538658322665 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.696442122802738 0.607115754394525 0.303557877197262 11 0.53792572751494 0.924148544970119 0.462074272485060 12 0.850963278509345 0.298073442981309 0.149036721490655 13 0.940902498584194 0.118195002831613 0.0590975014158064 14 0.931284248281702 0.137431503436597 0.0687157517182983 15 0.910768773164948 0.178462453670104 0.0892312268350519 16 0.8636714279847 0.272657144030599 0.136328572015300 17 0.819971844209926 0.360056311580149 0.180028155790075 18 0.752655960579425 0.49468807884115 0.247344039420575 19 0.705444200621708 0.589111598756584 0.294555799378292 20 0.640323450794565 0.719353098410869 0.359676549205435 21 0.623587754339017 0.752824491321965 0.376412245660983 22 0.62502325619457 0.74995348761086 0.37497674380543 23 0.574518482365942 0.850963035268115 0.425481517634058 24 0.673366711830903 0.653266576338195 0.326633288169097 25 0.856160348126132 0.287679303747736 0.143839651873868 26 0.817893234608958 0.364213530782084 0.182106765391042 27 0.76411664813137 0.471766703737261 0.235883351868630 28 0.761231861278298 0.477536277443403 0.238768138721702 29 0.705111840640208 0.589776318719584 0.294888159359792 30 0.766453938823413 0.467092122353174 0.233546061176587 31 0.714121542398787 0.571756915202427 0.285878457601213 32 0.649614026173885 0.70077194765223 0.350385973826115 33 0.624795320309719 0.750409359380562 0.375204679690281 34 0.635039891531734 0.729920216936532 0.364960108468266 35 0.563567491614611 0.872865016770778 0.436432508385389 36 0.717923974016252 0.564152051967497 0.282076025983748 37 0.651897695708635 0.696204608582729 0.348102304291365 38 0.600707442184682 0.798585115630636 0.399292557815318 39 0.523401398515106 0.953197202969787 0.476598601484894 40 0.461155713132765 0.92231142626553 0.538844286867235 41 0.565175415967456 0.869649168065088 0.434824584032544 42 0.551819130968122 0.896361738063757 0.448180869031878 43 0.532211069336306 0.935577861327387 0.467788930663694 44 0.47862043672933 0.95724087345866 0.52137956327067 45 0.601539757950262 0.796920484099476 0.398460242049738 46 0.611498529118671 0.777002941762658 0.388501470881329 47 0.640210876724787 0.719578246550427 0.359789123275213 48 0.6228977438332 0.7542045123336 0.3771022561668 49 0.647451543573989 0.705096912852023 0.352548456426011 50 0.561228834760717 0.877542330478565 0.438771165239283 51 0.542362601980793 0.915274796038415 0.457637398019207 52 0.455989233618351 0.911978467236703 0.544010766381649 53 0.458354138000893 0.916708276001786 0.541645861999107 54 0.366074357403352 0.732148714806704 0.633925642596648 55 0.273985230331990 0.547970460663981 0.72601476966801 56 0.18901294364516 0.37802588729032 0.81098705635484 57 0.235279942516831 0.470559885033661 0.76472005748317 58 0.309669475034538 0.619338950069077 0.690330524965462 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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