*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: Mon, 27 Dec 2010 13:24:06 +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/27/t1293456147stg9r0g6muxqxk3.htm/, Retrieved Mon, 27 Dec 2010 14:22:27 +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/2010/Dec/27/t1293456147stg9r0g6muxqxk3.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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493 797 514 840 522 988 490 819 484 831 506 904 501 814 462 798 465 828 454 789 464 930 427 744 460 832 473 826 465 907 422 776 415 835 413 715 420 729 363 733 376 736 380 712 384 711 346 667 389 799 407 661 393 692 346 649 348 729 353 622 364 671 305 635 307 648 312 745 312 624 286 477 324 710 336 515 327 461 302 590 299 415 311 554 315 585 264 513 278 591 278 561 287 684 279 668 324 795 354 776 354 1 043 360 964 363 762 385 1 030 412 939 370 779 389 918 395 839 417 874 404 840

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation WLH[t] = + 177.639763836283 + 0.252711714524369Faill[t] + 21.5772015188484M1[t] + 56.2980395338837M2[t] + 80.456632646757M3[t] -18.4720070744498M4[t] + 163.989382126553M5[t] + 130.635585726218M6[t] -0.424051914170813M7[t] + 0.69803953388371M8[t] + 0.517563878459179M9[t] -3.30999115693777M10[t] -0.694158759944824M11[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) 177.639763836283 83.00979 2.14 0.037577 0.018789 Faill 0.252711714524369 0.089561 2.8217 0.006979 0.00349 M1 21.5772015188484 79.454389 0.2716 0.787144 0.393572 M2 56.2980395338837 79.013689 0.7125 0.479671 0.239836 M3 80.456632646757 79.236339 1.0154 0.315114 0.157557 M4 -18.4720070744498 79.054999 -0.2337 0.816264 0.408132 M5 163.989382126553 79.076005 2.0738 0.0436 0.0218 M6 130.635585726218 79.068805 1.6522 0.105165 0.052582 M7 -0.424051914170813 79.672535 -0.0053 0.995776 0.497888 M8 0.69803953388371 79.013689 0.0088 0.992989 0.496494 M9 0.517563878459179 78.988834 0.0066 0.9948 0.4974 M10 -3.30999115693777 79.118548 -0.0418 0.966807 0.483403 M11 -0.694158759944824 79.201919 -0.0088 0.993044 0.496522 Multiple Linear Regression - Regression Statistics Multiple R 0.535720737207058 R-squared 0.286996708273673 Adjusted R-squared 0.104953314641420 F-TEST (value) 1.57652910411809 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.131590032998452 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 124.818098916034 Sum Squared Residuals 732239.2173996 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 493 400.628201831054 92.3717981689464 2 514 446.215643570637 67.7843564293634 3 522 507.775570433116 14.2244295668836 4 490 366.138650957291 123.861349042709 5 484 551.632580732586 -67.6325807325862 6 506 536.726739492531 -30.7267394925310 7 501 382.923047544948 118.076952455052 8 462 380.001751560613 81.9982484393869 9 465 387.402627340920 77.5973726590804 10 454 373.719315439072 80.2806845609278 11 464 411.967499584001 52.0325004159988 12 427 365.657279442413 61.3427205575866 13 460 409.473111839406 50.5268881605937 14 473 442.677679567295 30.3223204327046 15 465 487.305921556643 -22.3059215566425 16 422 355.272047232743 66.7279527672565 17 415 552.643427590684 -137.643427590684 18 413 488.964225447425 -75.9642254474251 19 420 361.442551810377 58.557448189623 20 363 363.575490116529 -0.575490116529059 21 376 364.153149604678 11.8468503953224 22 380 354.260513420696 25.7394865793042 23 384 356.623634103164 27.3763658968356 24 346 346.198477424037 -0.198477424036972 25 389 401.133625260102 -12.1336252601021 26 407 400.980246670774 6.01975332922552 27 393 432.972902933903 -39.9729029339031 28 346 323.177659488149 22.8223405118514 29 348 525.8559858511 -177.855985851100 30 353 465.462035996659 -112.462035996659 31 364 346.785272367964 17.2147276320364 32 305 338.809742093141 -33.8097420931409 33 307 341.914518726533 -34.9145187265332 34 312 362.6 -50.6 35 312 334.637714939544 -22.6377149395443 36 286 298.183251664407 -12.1832516644068 37 324 378.642282667433 -54.6422826674333 38 336 364.084336350217 -28.0843363502166 39 327 374.596496878774 -47.5964968787739 40 302 308.267668331211 -6.26766833121078 41 299 446.504507490449 -147.504507490449 42 311 448.277639409002 -137.277639409002 43 315 325.052064918868 -10.0520649188679 44 264 307.978912921168 -43.9789129211678 45 278 327.509950998644 -49.5099509986441 46 278 316.101044527516 -38.1010445275160 47 287 349.800417811006 -62.8004178110064 48 279 346.451189138561 -67.4511891385614 49 324 400.122778402005 -76.1227784020046 50 354 430.042093841077 -76.042093841077 51 354 258.349108197564 95.650891802436 52 43 250.143973990606 -207.143973990606 53 964 433.363498335181 530.636501664819 54 762 405.569359654383 356.430640345617 55 1 184.797063357843 -183.797063357843 56 412 415.634103308549 -3.63410330854913 57 370 375.019753329226 -5.01975332922552 58 389 406.319126612716 -17.3191266127159 59 395 388.970733562284 6.02926643771635 60 417 398.509802330581 18.4901976694186 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0145857347884705 0.029171469576941 0.98541426521153 17 0.0094737377100677 0.0189474754201354 0.990526262289932 18 0.00226054706366042 0.00452109412732083 0.99773945293634 19 0.000641273304351976 0.00128254660870395 0.999358726695648 20 0.000285748427474114 0.000571496854948227 0.999714251572526 21 6.96047594695208e-05 0.000139209518939042 0.99993039524053 22 1.51522081508307e-05 3.03044163016613e-05 0.99998484779185 23 7.19967661207058e-06 1.43993532241412e-05 0.999992800323388 24 1.87406247093655e-06 3.7481249418731e-06 0.99999812593753 25 2.1449814858749e-06 4.2899629717498e-06 0.999997855018514 26 4.78931829958751e-07 9.57863659917502e-07 0.99999952106817 27 1.44928984513214e-07 2.89857969026428e-07 0.999999855071016 28 4.28399559659662e-08 8.56799119319323e-08 0.999999957160044 29 4.84938719848462e-08 9.69877439696924e-08 0.999999951506128 30 1.74861735399429e-08 3.49723470798859e-08 0.999999982513826 31 6.11674134169305e-09 1.22334826833861e-08 0.999999993883259 32 1.51965910164231e-09 3.03931820328461e-09 0.99999999848034 33 3.77264437075154e-10 7.54528874150309e-10 0.999999999622736 34 1.06961362236647e-09 2.13922724473293e-09 0.999999998930386 35 2.00247362071609e-10 4.00494724143217e-10 0.999999999799753 36 4.76259364228288e-11 9.52518728456576e-11 0.999999999952374 37 2.45928571174157e-11 4.91857142348315e-11 0.999999999975407 38 4.89152739269325e-12 9.7830547853865e-12 0.999999999995108 39 7.62263144215197e-12 1.52452628843039e-11 0.999999999992377 40 2.60108710755317e-12 5.20217421510635e-12 0.999999999997399 41 9.62712989424022e-08 1.92542597884804e-07 0.999999903728701 42 0.565031806539599 0.869936386920802 0.434968193460401 43 0.668522020186256 0.662955959627489 0.331477979813744 44 0.555799816665779 0.888400366668443 0.444200183334221 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.827586206896552 NOK 5% type I error level 26 0.896551724137931 NOK 10% type I error level 26 0.896551724137931 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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