probeersel

*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: Sun, 19 Dec 2010 08:22:34 +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/19/t12927468916d12s2x4ibsad3z.htm/, Retrieved Sun, 19 Dec 2010 09:21:34 +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/19/t12927468916d12s2x4ibsad3z.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 «

0 0 104,7 102,8 0 113,9 0 0 113,2 105,9 108,8 102,3 0 100,7 115,5 100,7 109,9 114,6 0 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 0 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 0 0 116,8 115,7 0 0 0 0 103,1 0 0 102,7 0 0 104,5 105,1 0 0 0 0 111,5 0 0 111,7 0 0

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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation productie*dummy[t] = + 94.7630816505707 -0.785332289956865t + 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) 94.7630816505707 12.73755 7.4397 0 0 t -0.785332289956865 0.320905 -2.4472 0.017065 0.008532 Multiple Linear Regression - Regression Statistics Multiple R 0.288432188539708 R-squared 0.0831931273858054 Adjusted R-squared 0.0693021141643783 F-TEST (value) 5.98898914425322 F-TEST (DF numerator) 1 F-TEST (DF denominator) 66 p-value 0.0170646975583272 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 51.9400629338067 Sum Squared Residuals 178052.829079475 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 93.9777493606139 -93.9777493606139 2 0 93.192417070657 -93.192417070657 3 104.7 92.4070847807 12.2929152192999 4 102.8 91.6217524907432 11.1782475092568 5 0 90.8364202007863 -90.8364202007863 6 113.9 90.0510879108295 23.8489120891705 7 0 89.2657556208726 -89.2657556208726 8 0 88.4804233309158 -88.4804233309158 9 113.2 87.6950910409589 25.5049089590411 10 105.9 86.909758751002 18.990241248998 11 108.8 86.1244264610452 22.6755735389548 12 102.3 85.3390941710883 16.9609058289117 13 0 84.5537618811314 -84.5537618811314 14 100.7 83.7684295911746 16.9315704088254 15 115.5 82.9830973012177 32.5169026987823 16 100.7 82.1977650112608 18.5022349887392 17 109.9 81.412432721304 28.487567278696 18 114.6 80.6271004313471 33.9728995686529 19 0 79.8417681413902 -79.8417681413902 20 100.5 79.0564358514334 21.4435641485666 21 114.8 78.2711035614765 36.5288964385235 22 116.5 77.4857712715196 39.0142287284804 23 112.9 76.7004389815628 36.1995610184372 24 102 75.9151066916059 26.0848933083941 25 106 75.129774401649 30.870225598351 26 105.3 74.3444421116922 30.9555578883078 27 118.8 73.5591098217353 45.2408901782647 28 106.1 72.7737775317784 33.3262224682215 29 109.3 71.9884452418216 37.3115547581784 30 117.2 71.2031129518647 45.9968870481353 31 0 70.4177806619079 -70.4177806619079 32 104.2 69.632448371951 34.567551628049 33 112.5 68.8471160819941 43.6528839180059 34 122.4 68.0617837920373 54.3382162079628 35 113.3 67.2764515020804 46.0235484979196 36 100 66.4911192121235 33.5088807878765 37 110.7 65.7057869221667 44.9942130778333 38 112.8 64.9204546322098 47.8795453677902 39 109.8 64.1351223422529 45.6648776577471 40 117.3 63.3497900522961 53.9502099477039 41 109.1 62.5644577623392 46.5355422376608 42 115.9 61.7791254723823 54.1208745276177 43 0 60.9937931824255 -60.9937931824255 44 0 60.2084608924686 -60.2084608924686 45 116.8 59.4231286025117 57.3768713974883 46 115.7 58.6377963125549 57.0622036874451 47 0 57.852464022598 -57.852464022598 48 0 57.0671317326411 -57.0671317326411 49 0 56.2817994426843 -56.2817994426843 50 0 55.4964671527274 -55.4964671527274 51 103.1 54.7111348627705 48.3888651372294 52 0 53.9258025728137 -53.9258025728137 53 0 53.1404702828568 -53.1404702828568 54 102.7 52.3551379929 50.3448620071 55 0 51.5698057029431 -51.5698057029431 56 0 50.7844734129862 -50.7844734129862 57 104.5 49.9991411230294 54.5008588769706 58 105.1 49.2138088330725 55.8861911669275 59 0 48.4284765431156 -48.4284765431156 60 0 47.6431442531588 -47.6431442531588 61 0 46.8578119632019 -46.8578119632019 62 0 46.072479673245 -46.072479673245 63 111.5 45.2871473832882 66.2128526167118 64 0 44.5018150933313 -44.5018150933313 65 0 43.7164828033744 -43.7164828033744 66 111.7 42.9311505134176 68.7688494865824 67 0 42.1458182234607 -42.1458182234607 68 0 41.3604859335038 -41.3604859335038 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.809996771565448 0.380006456869104 0.190003228434552 6 0.716730932367813 0.566538135264374 0.283269067632187 7 0.844997261633838 0.310005476732323 0.155002738366162 8 0.864119351464748 0.271761297070503 0.135880648535252 9 0.868567334693779 0.262865330612442 0.131432665306221 10 0.821276822630803 0.357446354738394 0.178723177369197 11 0.75332006153032 0.493359876939361 0.246679938469681 12 0.669175953107508 0.661648093784984 0.330824046892492 13 0.862687078205851 0.274625843588298 0.137312921794149 14 0.813318298285985 0.37336340342803 0.186681701714015 15 0.757460913498252 0.485078173003497 0.242539086501748 16 0.687333395172709 0.625333209654582 0.312666604827291 17 0.609192374836341 0.781615250327317 0.390807625163659 18 0.527126768795227 0.945746462409546 0.472873231204773 19 0.814897964247425 0.370204071505151 0.185102035752575 20 0.761815712269859 0.476368575460283 0.238184287730141 21 0.700844466028496 0.598311067943007 0.299155533971504 22 0.632442358227148 0.735115283545703 0.367557641772852 23 0.558581060886977 0.882837878226046 0.441418939113023 24 0.488328061429034 0.976656122858068 0.511671938570966 25 0.416494880488371 0.832989760976743 0.583505119511629 26 0.348597503113794 0.697195006227588 0.651402496886206 27 0.283383287127605 0.566766574255209 0.716616712872395 28 0.227944529070285 0.455889058140569 0.772055470929715 29 0.178684591464977 0.357369182929954 0.821315408535023 30 0.136959409913407 0.273918819826814 0.863040590086593 31 0.406452861372414 0.812905722744827 0.593547138627586 32 0.339396321327499 0.678792642654998 0.660603678672501 33 0.277267730058682 0.554535460117365 0.722732269941318 34 0.226934445697169 0.453868891394338 0.773065554302831 35 0.180298029700432 0.360596059400864 0.819701970299568 36 0.141200607493392 0.282401214986784 0.858799392506608 37 0.109763678423857 0.219527356847714 0.890236321576143 38 0.0863708669524688 0.172741733904938 0.913629133047531 39 0.0687129343523899 0.13742586870478 0.93128706564761 40 0.0597334637597941 0.119466927519588 0.940266536240206 41 0.0532891536985625 0.106578307397125 0.946710846301438 42 0.0569577843931425 0.113915568786285 0.943042215606858 43 0.129664315056643 0.259328630113286 0.870335684943357 44 0.206943565470037 0.413887130940074 0.793056434529963 45 0.224119058439781 0.448238116879562 0.775880941560219 46 0.283198788859757 0.566397577719515 0.716801211140243 47 0.334137414491738 0.668274828983476 0.665862585508262 48 0.365206488301233 0.730412976602465 0.634793511698768 49 0.385013945110127 0.770027890220253 0.614986054889873 50 0.402782395024974 0.805564790049949 0.597217604975026 51 0.409073690617466 0.818147381234932 0.590926309382534 52 0.404249205184822 0.808498410369643 0.595750794815178 53 0.408968944856879 0.817937889713757 0.591031055143121 54 0.410654368905895 0.82130873781179 0.589345631094105 55 0.393143653047839 0.786287306095678 0.606856346952161 56 0.400544294517668 0.801088589035337 0.599455705482332 57 0.395354414656968 0.790708829313936 0.604645585343032 58 0.513859372326333 0.972281255347334 0.486140627673667 59 0.424704681403351 0.849409362806703 0.575295318596649 60 0.341077702854404 0.682155405708808 0.658922297145596 61 0.281064209143251 0.562128418286502 0.718935790856749 62 0.288231390636202 0.576462781272403 0.711768609363798 63 0.307049195822996 0.614098391645992 0.692950804177004 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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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