*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, 14 Dec 2009 14:20:32 -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/14/t1260828361fbhlbspswc1jr9t.htm/, Retrieved Mon, 14 Dec 2009 23:06:13 +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/14/t1260828361fbhlbspswc1jr9t.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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564 -0,9 581 -1 597 -0,7 587 -1,7 536 -1 524 -0,2 537 0,7 536 0,6 533 1,9 528 2,1 516 2,7 502 3,2 506 4,8 518 5,5 534 5,4 528 5,9 478 5,8 469 5,1 490 4,1 493 4,4 508 3,6 517 3,5 514 3,1 510 2,9 527 2,2 542 1,4 565 1,2 555 1,3 499 1,3 511 1,3 526 1,8 532 1,8 549 1,8 561 1,7 557 2,1 566 2 588 1,7 620 1,9 626 2,3 620 2,4 573 2,5 573 2,8 574 2,6 580 2,2 590 2,8 593 2,8 597 2,8 595 2,3 612 2,2 628 3 629 2,9 621 2,7 569 2,7 567 2,3 573 2,4 584 2,8 589 2,3 591 2 595 1,9 594 2,3

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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 575.794215296264 -8.46459087328886X[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) 575.794215296264 8.947963 64.3492 0 0 X -8.46459087328886 3.199683 -2.6454 0.010482 0.005241 Multiple Linear Regression - Regression Statistics Multiple R 0.32813137651715 R-squared 0.107670200255040 Adjusted R-squared 0.0922852037077129 F-TEST (value) 6.99838962744175 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0104815890361800 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 39.2464920077563 Sum Squared Residuals 89336.6538250631 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 564 583.412347082225 -19.4123470822246 2 581 584.258806169553 -3.25880616955296 3 597 581.719428907566 15.2805710924337 4 587 590.184019780855 -3.18401978085519 5 536 584.258806169553 -48.258806169553 6 524 577.487133470922 -53.4871334709219 7 537 569.869001684962 -32.8690016849619 8 536 570.715460772291 -34.7154607722908 9 533 559.711492637015 -26.7114926370153 10 528 558.018574462357 -30.0185744623575 11 516 552.939819938384 -36.9398199383842 12 502 548.70752450174 -46.7075245017398 13 506 535.164179104478 -29.1641791044776 14 518 529.238965493175 -11.2389654931754 15 534 530.085424580504 3.91457541949569 16 528 525.85312914386 2.14687085614012 17 478 526.699588231189 -48.6995882311888 18 469 532.624801842491 -63.624801842491 19 490 541.08939271578 -51.0893927157798 20 493 538.550015453793 -45.5500154537932 21 508 545.321688152424 -37.3216881524243 22 517 546.168147239753 -29.1681472397531 23 514 549.553983589069 -35.5539835890687 24 510 551.246901763726 -41.2469017637265 25 527 557.172115375029 -30.1721153750287 26 542 563.94378807366 -21.9437880736597 27 565 565.636706248318 -0.63670624831751 28 555 564.790247160989 -9.79024716098862 29 499 564.790247160989 -65.7902471609886 30 511 564.790247160989 -53.7902471609886 31 526 560.557951724344 -34.5579517243442 32 532 560.557951724344 -28.5579517243442 33 549 560.557951724344 -11.5579517243442 34 561 561.404410811673 -0.404410811673082 35 557 558.018574462357 -1.01857446235754 36 566 558.865033549686 7.13496645031357 37 588 561.404410811673 26.5955891883269 38 620 559.711492637015 60.2885073629847 39 626 556.3256562877 69.6743437123002 40 620 555.479197200371 64.5208027996291 41 573 554.632738113042 18.367261886958 42 573 552.093360851055 20.9066391489447 43 574 553.786279025713 20.2137209742869 44 580 557.172115375029 22.8278846249713 45 590 552.093360851055 37.9066391489447 46 593 552.093360851055 40.9066391489447 47 597 552.093360851055 44.9066391489447 48 595 556.3256562877 38.6743437123002 49 612 557.172115375029 54.8278846249713 50 628 550.400442676398 77.5995573236024 51 629 551.246901763726 77.7530982362735 52 621 552.939819938384 68.0601800616158 53 569 552.939819938384 16.0601800616158 54 567 556.3256562877 10.6743437123002 55 573 555.479197200371 17.5208027996291 56 584 552.093360851055 31.9066391489447 57 589 556.3256562877 32.6743437123002 58 591 558.865033549686 32.1349664503136 59 595 559.711492637015 35.2885073629847 60 594 556.3256562877 37.6743437123002 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.293053411647159 0.586106823294317 0.706946588352841 6 0.252197271767784 0.504394543535569 0.747802728232216 7 0.162096251173404 0.324192502346808 0.837903748826596 8 0.093340284724319 0.186680569448638 0.906659715275681 9 0.0631565793193668 0.126313158638734 0.936843420680633 10 0.0351022738030365 0.0702045476060731 0.964897726196963 11 0.0182645646616362 0.0365291293232725 0.981735435338364 12 0.0097055088676228 0.0194110177352456 0.990294491132377 13 0.0063450552391089 0.0126901104782178 0.99365494476089 14 0.00633404778264708 0.0126680955652942 0.993665952217353 15 0.00769985615426848 0.0153997123085370 0.992300143845732 16 0.00599004133830572 0.0119800826766114 0.994009958661694 17 0.00567615052688818 0.0113523010537764 0.994323849473112 18 0.0103412372856806 0.0206824745713612 0.98965876271432 19 0.0112444829264333 0.0224889658528666 0.988755517073567 20 0.0135205121661481 0.0270410243322961 0.986479487833852 21 0.0159177845511851 0.0318355691023703 0.984082215448815 22 0.0220024396065571 0.0440048792131143 0.977997560393443 23 0.0413074702114925 0.082614940422985 0.958692529788507 24 0.121017165428479 0.242034330856958 0.878982834571521 25 0.141610461398237 0.283220922796474 0.858389538601763 26 0.104043901968828 0.208087803937656 0.895956098031172 27 0.117117462109222 0.234234924218445 0.882882537890778 28 0.09926449907241 0.19852899814482 0.90073550092759 29 0.189250618302543 0.378501236605087 0.810749381697457 30 0.239099404301692 0.478198808603384 0.760900595698308 31 0.293165219867562 0.586330439735124 0.706834780132438 32 0.361045980334563 0.722091960669126 0.638954019665437 33 0.39363716141759 0.78727432283518 0.60636283858241 34 0.41968711214218 0.83937422428436 0.58031288785782 35 0.504404939330806 0.991190121338387 0.495595060669194 36 0.577405784449691 0.845188431100619 0.422594215550309 37 0.65631333733977 0.687373325320461 0.343686662660231 38 0.88768709967107 0.224625800657859 0.112312900328929 39 0.977911847428664 0.0441763051426714 0.0220881525713357 40 0.99330848801328 0.0133830239734392 0.00669151198671958 41 0.992394455972025 0.0152110880559505 0.00760554402797526 42 0.993342513671758 0.0133149726564843 0.00665748632824217 43 0.993267314865696 0.0134653702686082 0.00673268513430412 44 0.98970797511703 0.0205840497659411 0.0102920248829705 45 0.986633901644707 0.0267321967105852 0.0133660983552926 46 0.98171408738287 0.0365718252342589 0.0182859126171295 47 0.9737619487723 0.0524761024553989 0.0262380512276994 48 0.958347455716785 0.0833050885664301 0.0416525442832151 49 0.96004137392004 0.07991725215992 0.03995862607996 50 0.963061294283405 0.0738774114331906 0.0369387057165953 51 0.983440896042335 0.0331182079153303 0.0165591039576652 52 0.998753717058698 0.00249256588260383 0.00124628294130192 53 0.99600391155142 0.00799217689715946 0.00399608844857973 54 0.9973627001683 0.00527459966340169 0.00263729983170084 55 0.999532882210638 0.000934235578723056 0.000467117789361528 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.0784313725490196 NOK 5% type I error level 25 0.490196078431373 NOK 10% type I error level 31 0.607843137254902 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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