Model_1

*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 08:59:24 -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/t125873287591n3c748jdtrsse.htm/, Retrieved Fri, 20 Nov 2009 17:01:27 +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/t125873287591n3c748jdtrsse.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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562 573 561 572 555 566 544 555 537 548 543 554 594 605 611 622 613 624 611 622 594 605 595 606 591 602 589 600 584 595 573 584 567 578 569 580 621 632 629 640 628 639 612 623 595 606 597 608 593 604 590 601 580 591 574 585 573 584 573 584 620 631 626 637 620 631 588 599 566 577 557 568 561 572 549 560 532 543 526 537 511 522 499 510 555 566 565 576 542 553 527 538 510 521 514 525 517 528 508 519 493 504 490 501 469 480 478 489 528 539 534 545 518 529 506 517 502 513 516 527 528 539

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] = -10.9999999999998 + 1X[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) -10.9999999999998 0 -54235051562800.9 0 0 X 1 0 2818919394784156 0 0 Multiple Linear Regression - Regression Statistics Multiple R 1 R-squared 1 Adjusted R-squared 1 F-TEST (value) 7.94630655429027e+30 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.14906334931848e-13 Sum Squared Residuals 7.79004482640727e-25 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 562 561.999999999999 8.7498286696373e-13 2 561 561 -1.27465237899230e-14 3 555 555 -1.45839977517006e-14 4 544 544 -1.43481736451483e-14 5 537 537 -1.72663564817609e-14 6 543 543 -1.57801179586074e-14 7 594 594 -1.20288747088037e-14 8 611 611 -1.78838876498035e-14 9 613 613 -1.14672853440849e-14 10 611 611 -1.78838876498035e-14 11 594 594 -1.20288747088037e-14 12 595 595 -1.94787145923459e-14 13 591 591 -1.45483508097808e-14 14 589 589 -1.38595257578984e-14 15 584 584 -1.56901768069931e-14 16 573 573 -1.54543527004408e-14 17 567 567 -1.42760559644939e-14 18 569 569 -1.40767025966762e-14 19 621 621 -1.42225855516142e-14 20 629 629 -2.40833131167445e-14 21 628 628 -9.52804587560131e-15 22 612 612 -1.11228728181437e-14 23 595 595 -1.94787145923459e-14 24 597 597 -2.01675396442282e-14 25 593 593 -1.87898895404636e-14 26 590 590 -1.42039382838396e-14 27 580 580 -1.78652403820289e-14 28 574 574 -1.57987652263820e-14 29 573 573 -1.54543527004408e-14 30 573 573 -1.54543527004408e-14 31 620 620 -1.3878173025673e-14 32 626 626 -2.3050075538921e-14 33 620 620 -1.3878173025673e-14 34 588 588 -1.35151132319573e-14 35 566 566 -1.48198218582529e-14 36 557 557 -1.39405551740327e-14 37 561 561 -1.44300268580973e-14 38 549 549 -1.25175225960536e-14 39 532 532 -1.19915801732546e-14 40 526 526 -9.9251050176076e-15 41 511 511 -1.18643444860911e-14 42 499 499 -7.73139417479719e-15 43 555 555 -1.45839977517006e-14 44 565 565 -1.44754093323117e-14 45 542 542 -1.54357054326662e-14 46 527 527 -1.73749449011498e-14 47 510 510 -1.151993196015e-14 48 514 514 -1.28975820639146e-14 49 517 517 -1.39308196417381e-14 50 508 508 -1.08311069082677e-14 51 493 493 -1.98757737343522e-14 52 490 490 -1.88425361565287e-14 53 469 469 -1.16098731117643e-14 54 478 478 -1.47095858452347e-14 55 528 528 -1.06139300694899e-14 56 534 534 -1.26804052251369e-14 57 518 518 -7.16980481007829e-15 58 506 506 -1.72477092139863e-14 59 502 502 -1.58700591102217e-14 60 516 516 -1.35864071157970e-14 61 528 528 -1.06139300694899e-14 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 1.03471779602571e-06 2.06943559205142e-06 0.999998965282204 6 0.000474485593374027 0.000948971186748055 0.999525514406626 7 1 1.01113848317708e-35 5.05569241588539e-36 8 0.674471505154387 0.651056989691226 0.325528494845613 9 1 8.65796250173894e-61 4.32898125086947e-61 10 4.84201941228151e-05 9.68403882456302e-05 0.999951579805877 11 1 5.25540310806625e-56 2.62770155403313e-56 12 2.79778802958151e-15 5.59557605916302e-15 0.999999999999997 13 0.999489838279317 0.00102032344136618 0.000510161720683091 14 0.434510781218193 0.869021562436385 0.565489218781807 15 0.561095195041889 0.877809609916222 0.438904804958111 16 3.86802413799862e-23 7.73604827599725e-23 1 17 1.94159059550450e-22 3.88318119100901e-22 1 18 1.11166999174810e-40 2.22333998349621e-40 1 19 0.593840627452085 0.81231874509583 0.406159372547915 20 1 2.95888856202590e-83 1.47944428101295e-83 21 0.938229111038922 0.123541777922157 0.0617708889610783 22 0.999919187930865 0.000161624138270833 8.08120691354164e-05 23 0.999869478569238 0.000261042861523580 0.000130521430761790 24 0.999872120599961 0.000255758800077084 0.000127879400038542 25 3.24024184322771e-32 6.48048368645542e-32 1 26 3.62790035365853e-25 7.25580070731706e-25 1 27 1 6.49723521571497e-35 3.24861760785749e-35 28 1 1.14724398879949e-54 5.73621994399743e-55 29 1 9.85796444983566e-17 4.92898222491783e-17 30 3.9387900015696e-07 7.8775800031392e-07 0.999999606121 31 2.94926964189101e-45 5.89853928378202e-45 1 32 0.00238187010666648 0.00476374021333296 0.997618129893334 33 1 3.38453029540524e-17 1.69226514770262e-17 34 0.00489840222498825 0.0097968044499765 0.995101597775012 35 0.999752407214779 0.000495185570442931 0.000247592785221466 36 7.40160208070831e-48 1.48032041614166e-47 1 37 0.000251804553765988 0.000503609107531977 0.999748195446234 38 0.486015155289995 0.97203031057999 0.513984844710005 39 1 3.38926834391317e-28 1.69463417195658e-28 40 7.60318929450352e-20 1.52063785890070e-19 1 41 1 1.56218266805104e-24 7.81091334025521e-25 42 1 3.6889737533062e-36 1.8444868766531e-36 43 1 4.50999965680094e-23 2.25499982840047e-23 44 0.00065906129136285 0.0013181225827257 0.999340938708637 45 1 4.49029208836164e-22 2.24514604418082e-22 46 0.999999999999909 1.82812310516569e-13 9.14061552582847e-14 47 1 1.26654086808440e-17 6.33270434042201e-18 48 8.47779184640072e-33 1.69555836928014e-32 1 49 0.0236951910294237 0.0473903820588474 0.976304808970576 50 1.0560877894018e-54 2.1121755788036e-54 1 51 0.00124790297786906 0.00249580595573813 0.99875209702213 52 0.999999999762462 4.75075007704935e-10 2.37537503852467e-10 53 3.33493002470245e-45 6.6698600494049e-45 1 54 0.923839355451948 0.152321289096104 0.0761606445480518 55 0.948310692046408 0.103378615907185 0.0516893079535924 56 0.298632516488587 0.597265032977174 0.701367483511413 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 42 0.807692307692308 NOK 5% type I error level 43 0.826923076923077 NOK 10% type I error level 43 0.826923076923077 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/10e7g51258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/10e7g51258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/194q61258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/194q61258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/21gp41258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/21gp41258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/3irly1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/3irly1258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/4aott1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/4aott1258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/5npga1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/5npga1258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/6acsl1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/6acsl1258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/7g2dj1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/7g2dj1258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/86awc1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/86awc1258732760.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/9e5kh1258732760.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t125873287591n3c748jdtrsse/9e5kh1258732760.ps (open in new window)

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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