Workshop 7

*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: Thu, 19 Nov 2009 12:18:42 -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/19/t1258658424u60fyj2vz4drka2.htm/, Retrieved Thu, 19 Nov 2009 20:20:36 +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/19/t1258658424u60fyj2vz4drka2.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:

Workshop 7 link 2

Dataseries X:

» Textbox « » Textfile « » CSV «

449 0 452 0 462 0 455 0 461 0 461 0 463 0 462 0 456 0 455 0 456 0 472 0 472 0 471 0 465 0 459 0 465 0 468 0 467 0 463 0 460 0 462 0 461 0 476 0 476 0 471 0 453 0 443 0 442 0 444 0 438 0 427 0 424 0 416 0 406 0 431 0 434 0 418 0 412 0 404 0 409 0 412 1 406 1 398 1 397 1 385 1 390 1 413 1 413 1 401 1 397 1 397 1 409 1 419 1 424 1 428 1 430 1 424 1 433 1 456 1 459 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 464.210309278351 -36.5257731958763X[t] -1.53505154639171M1[t] -14.3051546391753M2[t] -19.1051546391753M3[t] -25.3051546391753M4[t] -19.7051546391753M5[t] -8.80000000000004M6[t] -10.0000000000000M7[t] -14.0000000000000M8[t] -16.2000000000000M9[t] -21.2000000000000M10[t] -20.4000000000000M11[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) 464.210309278351 9.70414 47.8363 0 0 X -36.5257731958763 5.855367 -6.238 0 0 M1 -1.53505154639171 12.756997 -0.1203 0.904724 0.452362 M2 -14.3051546391753 13.369397 -1.07 0.289974 0.144987 M3 -19.1051546391753 13.369397 -1.429 0.159474 0.079737 M4 -25.3051546391753 13.369397 -1.8928 0.064427 0.032214 M5 -19.7051546391753 13.369397 -1.4739 0.147037 0.073519 M6 -8.80000000000004 13.318009 -0.6608 0.511926 0.255963 M7 -10.0000000000000 13.318009 -0.7509 0.456401 0.2282 M8 -14.0000000000000 13.318009 -1.0512 0.298427 0.149213 M9 -16.2000000000000 13.318009 -1.2164 0.229781 0.114891 M10 -21.2000000000000 13.318009 -1.5918 0.117988 0.058994 M11 -20.4000000000000 13.318009 -1.5318 0.132146 0.066073 Multiple Linear Regression - Regression Statistics Multiple R 0.697897034627074 R-squared 0.487060270941264 Adjusted R-squared 0.35882533867658 F-TEST (value) 3.79818714245463 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.000447445226957166 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.0576217111663 Sum Squared Residuals 21284.3247422680 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 449 462.675257731958 -13.6752577319584 2 452 449.905154639175 2.09484536082474 3 462 445.105154639175 16.8948453608247 4 455 438.905154639175 16.0948453608247 5 461 444.505154639175 16.4948453608247 6 461 455.410309278350 5.58969072164948 7 463 454.210309278351 8.78969072164944 8 462 450.210309278351 11.7896907216495 9 456 448.010309278351 7.98969072164949 10 455 443.010309278351 11.9896907216495 11 456 443.810309278351 12.1896907216495 12 472 464.210309278351 7.78969072164946 13 472 462.675257731959 9.32474226804115 14 471 449.905154639175 21.0948453608248 15 465 445.105154639175 19.8948453608247 16 459 438.905154639175 20.0948453608248 17 465 444.505154639175 20.4948453608247 18 468 455.410309278350 12.5896907216495 19 467 454.210309278351 12.7896907216495 20 463 450.210309278351 12.7896907216495 21 460 448.010309278351 11.9896907216495 22 462 443.010309278351 18.9896907216495 23 461 443.810309278351 17.1896907216495 24 476 464.210309278351 11.7896907216495 25 476 462.675257731959 13.3247422680412 26 471 449.905154639175 21.0948453608248 27 453 445.105154639175 7.89484536082474 28 443 438.905154639175 4.09484536082476 29 442 444.505154639175 -2.50515463917525 30 444 455.410309278350 -11.4103092783505 31 438 454.210309278351 -16.2103092783505 32 427 450.210309278351 -23.2103092783505 33 424 448.010309278351 -24.0103092783505 34 416 443.010309278351 -27.0103092783505 35 406 443.810309278351 -37.8103092783505 36 431 464.210309278351 -33.2103092783505 37 434 462.675257731959 -28.6752577319588 38 418 449.905154639175 -31.9051546391752 39 412 445.105154639175 -33.1051546391753 40 404 438.905154639175 -34.9051546391753 41 409 444.505154639175 -35.5051546391753 42 412 418.884536082474 -6.88453608247421 43 406 417.684536082474 -11.6845360824742 44 398 413.684536082474 -15.6845360824742 45 397 411.484536082474 -14.4845360824742 46 385 406.484536082474 -21.4845360824742 47 390 407.284536082474 -17.2845360824742 48 413 427.684536082474 -14.6845360824742 49 413 426.149484536083 -13.1494845360825 50 401 413.379381443299 -12.3793814432990 51 397 408.579381443299 -11.5793814432990 52 397 402.379381443299 -5.37938144329894 53 409 407.979381443299 1.02061855670105 54 419 418.884536082474 0.115463917525785 55 424 417.684536082474 6.31546391752579 56 428 413.684536082474 14.3154639175258 57 430 411.484536082474 18.5154639175258 58 424 406.484536082474 17.5154639175258 59 433 407.284536082474 25.7154639175258 60 456 427.684536082474 28.3154639175258 61 459 426.149484536083 32.8505154639175 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.171119689225042 0.342239378450084 0.828880310774958 17 0.0809937872773374 0.161987574554675 0.919006212722663 18 0.0372396524716644 0.0744793049433289 0.962760347528336 19 0.0155662925136809 0.0311325850273618 0.984433707486319 20 0.00610497850661368 0.0122099570132274 0.993895021493386 21 0.00240693510760585 0.0048138702152117 0.997593064892394 22 0.00126118051161665 0.0025223610232333 0.998738819488383 23 0.000634685930299165 0.00126937186059833 0.9993653140697 24 0.000279545119564017 0.000559090239128033 0.999720454880436 25 0.000426639864159739 0.000853279728319478 0.99957336013584 26 0.000673345278685245 0.00134669055737049 0.999326654721315 27 0.000932206404180965 0.00186441280836193 0.999067793595819 28 0.00172456218898512 0.00344912437797023 0.998275437811015 29 0.00503253462350133 0.0100650692470027 0.994967465376499 30 0.00879340747973921 0.0175868149594784 0.99120659252026 31 0.0207874743458941 0.0415749486917883 0.979212525654106 32 0.057413879623699 0.114827759247398 0.9425861203763 33 0.0918919017417304 0.183783803483461 0.90810809825827 34 0.165376083083269 0.330752166166539 0.83462391691673 35 0.294010424901188 0.588020849802375 0.705989575098812 36 0.332576511405207 0.665153022810414 0.667423488594793 37 0.313818405133949 0.627636810267898 0.686181594866051 38 0.343357146095348 0.686714292190697 0.656642853904652 39 0.355586611322099 0.711173222644197 0.644413388677901 40 0.342928847491742 0.685857694983484 0.657071152508258 41 0.307275919099733 0.614551838199467 0.692724080900267 42 0.210059602105094 0.420119204210189 0.789940397894906 43 0.140936355948545 0.281872711897091 0.859063644051455 44 0.103187398181657 0.206374796363315 0.896812601818343 45 0.0746860518364164 0.149372103672833 0.925313948163584 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.266666666666667 NOK 5% type I error level 13 0.433333333333333 NOK 10% type I error level 14 0.466666666666667 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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