paperMR1

*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, 24 Dec 2010 17:02:28 +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/24/t1293210011tpc8rp5ws9yb3l3.htm/, Retrieved Fri, 24 Dec 2010 18:00:13 +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/2010/Dec/24/t1293210011tpc8rp5ws9yb3l3.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:

» Textbox « » Textfile « » CSV «

595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 0 478 0 528 0 534 0 518 0 506 0 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 1 587 1 597 1 581 1 564 1 558 1 575 1 580 1 575 1 563 1 552 1 537 1 545 1 601 1 604 1 586 1 564 1 549 1

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 546.777777777778 + 10.4222222222222X[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) 546.777777777778 6.125578 89.2614 0 0 X 10.4222222222222 9.568458 1.0892 0.280483 0.140241 Multiple Linear Regression - Regression Statistics Multiple R 0.140400649383238 R-squared 0.0197123423472349 Adjusted R-squared 0.00309729730227293 F-TEST (value) 1.18641522149902 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.280482906615092 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36.7534668541673 Sum Squared Residuals 79698.2222222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 595 546.777777777778 48.2222222222221 2 597 546.777777777778 50.2222222222222 3 593 546.777777777778 46.2222222222222 4 590 546.777777777778 43.2222222222222 5 580 546.777777777778 33.2222222222222 6 574 546.777777777778 27.2222222222222 7 573 546.777777777778 26.2222222222222 8 573 546.777777777778 26.2222222222222 9 620 546.777777777778 73.2222222222222 10 626 546.777777777778 79.2222222222222 11 620 546.777777777778 73.2222222222222 12 588 546.777777777778 41.2222222222222 13 566 546.777777777778 19.2222222222222 14 557 546.777777777778 10.2222222222222 15 561 546.777777777778 14.2222222222222 16 549 546.777777777778 2.22222222222223 17 532 546.777777777778 -14.7777777777778 18 526 546.777777777778 -20.7777777777778 19 511 546.777777777778 -35.7777777777778 20 499 546.777777777778 -47.7777777777778 21 555 546.777777777778 8.22222222222223 22 565 546.777777777778 18.2222222222222 23 542 546.777777777778 -4.77777777777777 24 527 546.777777777778 -19.7777777777778 25 510 546.777777777778 -36.7777777777778 26 514 546.777777777778 -32.7777777777778 27 517 546.777777777778 -29.7777777777778 28 508 546.777777777778 -38.7777777777778 29 493 546.777777777778 -53.7777777777778 30 490 546.777777777778 -56.7777777777778 31 469 546.777777777778 -77.7777777777778 32 478 546.777777777778 -68.7777777777778 33 528 546.777777777778 -18.7777777777778 34 534 546.777777777778 -12.7777777777778 35 518 546.777777777778 -28.7777777777778 36 506 546.777777777778 -40.7777777777778 37 502 557.2 -55.2 38 516 557.2 -41.2 39 528 557.2 -29.2 40 533 557.2 -24.2 41 536 557.2 -21.2 42 537 557.2 -20.2 43 524 557.2 -33.2 44 536 557.2 -21.2 45 587 557.2 29.8 46 597 557.2 39.8 47 581 557.2 23.8 48 564 557.2 6.8 49 558 557.2 0.8 50 575 557.2 17.8 51 580 557.2 22.8 52 575 557.2 17.8 53 563 557.2 5.8 54 552 557.2 -5.2 55 537 557.2 -20.2 56 545 557.2 -12.2 57 601 557.2 43.8 58 604 557.2 46.8 59 586 557.2 28.8 60 564 557.2 6.8 61 549 557.2 -8.2 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0136572279319022 0.0273144558638044 0.986342772068098 6 0.0126785013486781 0.0253570026973562 0.987321498651322 7 0.00784033686634269 0.0156806737326854 0.992159663133657 8 0.00402543190492543 0.00805086380985085 0.995974568095075 9 0.0258825655637577 0.0517651311275153 0.974117434436242 10 0.0868950674204658 0.173790134840932 0.913104932579534 11 0.149300716423715 0.29860143284743 0.850699283576285 12 0.131622058984033 0.263244117968067 0.868377941015967 13 0.163733656602231 0.327467313204461 0.83626634339777 14 0.231453874794798 0.462907749589596 0.768546125205202 15 0.271657700013777 0.543315400027553 0.728342299986223 16 0.362985129556974 0.725970259113948 0.637014870443026 17 0.541628787219132 0.916742425561736 0.458371212780868 18 0.687949076737073 0.624101846525853 0.312050923262927 19 0.836007108085927 0.327985783828146 0.163992891914073 20 0.931847655793392 0.136304688413216 0.0681523442066082 21 0.929506080114684 0.140987839770631 0.0704939198853155 22 0.942008365642593 0.115983268714815 0.0579916343574073 23 0.94382555073814 0.112348898523719 0.0561744492618594 24 0.947584656735592 0.104830686528817 0.0524153432644084 25 0.958521636739744 0.0829567265205111 0.0414783632602556 26 0.961601028190452 0.0767979436190965 0.0383989718095483 27 0.96117976250854 0.0776404749829194 0.0388202374914597 28 0.962645671132584 0.0747086577348317 0.0373543288674158 29 0.970571583586815 0.0588568328263703 0.0294284164131852 30 0.976342637653843 0.0473147246923137 0.0236573623461569 31 0.990710617848655 0.0185787643026905 0.00928938215134523 32 0.99519916226126 0.00960167547747934 0.00480083773873967 33 0.992248582492178 0.0155028350156439 0.00775141750782196 34 0.988522884118354 0.0229542317632916 0.0114771158816458 35 0.983101151694214 0.0337976966115726 0.0168988483057863 36 0.976701873856062 0.0465962522878754 0.0232981261439377 37 0.98706156837018 0.0258768632596413 0.0129384316298206 38 0.990304182715606 0.0193916345687879 0.00969581728439397 39 0.990301509823666 0.0193969803526686 0.0096984901763343 40 0.98939768289111 0.0212046342177812 0.0106023171088906 41 0.98800398402577 0.0239920319484592 0.0119960159742296 42 0.986761593515414 0.0264768129691718 0.0132384064845859 43 0.99282250747909 0.0143549850418213 0.00717749252091063 44 0.9944136288535 0.0111727422929994 0.00558637114649971 45 0.992958663968556 0.0140826720628882 0.00704133603144411 46 0.994072477807219 0.0118550443855623 0.00592752219278114 47 0.990297475316816 0.0194050493663677 0.00970252468318386 48 0.98121400795521 0.0375719840895796 0.0187859920447898 49 0.966935431317926 0.0661291373641472 0.0330645686820736 50 0.942219174429012 0.115561651141976 0.0577808255709878 51 0.908493188766796 0.183013622466408 0.0915068112332042 52 0.851412802852864 0.297174394294271 0.148587197147136 53 0.762342006250743 0.475315987498515 0.237657993749257 54 0.667295807105923 0.665408385788154 0.332704192894077 55 0.66577504787952 0.668449904240959 0.33422495212048 56 0.649153372358758 0.701693255282485 0.350846627641242 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0384615384615385 NOK 5% type I error level 23 0.442307692307692 NOK 10% type I error level 30 0.576923076923077 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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