Multiple lineair regression

*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: Sat, 22 Nov 2008 03:58:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/22/t122735216091ky2rd2hiatmom.htm/, Retrieved Sat, 22 Nov 2008 11:09:20 +0000

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/2008/Nov/22/t122735216091ky2rd2hiatmom.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

eigen dataset

Dataseries X:

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6,06 0 5,983 0 6,11 0 6,143 0 6,093 0 6,148 0 6,464 0 6,532 0 6,321 0 6,23 0 6,176 0 6,338 0 6,462 0 6,401 0 6,46 0 6,519 0 6,542 0 6,637 0 7,114 0 7,579 0 7,408 0 8,243 0 8,243 0 8,434 0 8,576 0 8,58 0 8,645 0 8,66 0 8,72 0 8,787 0 9,162 0 9,144 0 8,806 0 8,778 0 8,66 0 8,826 0 8,609 1 8,628 1 8,619 1 8,775 1 8,84 1 8,745 1 9,092 1 8,934 1 8,749 1 8,298 1 8,067 1 7,969 1 7,999 0 7,865 0 7,746 0 7,633 0 7,458 0 7,391 0 7,856 0 7,72 0 7,297 0 7,123 0 7,004 0 7,151 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Textiel[t] = + 7.42139583333333 + 1.18902083333333dummy[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) 7.42139583333333 0.134549 55.1576 0 0 dummy 1.18902083333333 0.300861 3.9521 0.000213 0.000106 Multiple Linear Regression - Regression Statistics Multiple R 0.460606011517861 R-squared 0.212157897846391 Adjusted R-squared 0.198574413326502 F-TEST (value) 15.6188125024721 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.000212839494328709 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.932182777658247 Sum Squared Residuals 50.3999543958334 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.06 7.42139583333334 -1.36139583333334 2 5.983 7.42139583333333 -1.43839583333333 3 6.11 7.42139583333333 -1.31139583333333 4 6.143 7.42139583333333 -1.27839583333333 5 6.093 7.42139583333333 -1.32839583333333 6 6.148 7.42139583333333 -1.27339583333333 7 6.464 7.42139583333333 -0.957395833333333 8 6.532 7.42139583333333 -0.889395833333333 9 6.321 7.42139583333333 -1.10039583333333 10 6.23 7.42139583333333 -1.19139583333333 11 6.176 7.42139583333333 -1.24539583333333 12 6.338 7.42139583333333 -1.08339583333333 13 6.462 7.42139583333333 -0.959395833333333 14 6.401 7.42139583333333 -1.02039583333333 15 6.46 7.42139583333333 -0.961395833333333 16 6.519 7.42139583333333 -0.902395833333333 17 6.542 7.42139583333333 -0.879395833333333 18 6.637 7.42139583333333 -0.784395833333334 19 7.114 7.42139583333333 -0.307395833333333 20 7.579 7.42139583333333 0.157604166666667 21 7.408 7.42139583333333 -0.0133958333333328 22 8.243 7.42139583333333 0.821604166666667 23 8.243 7.42139583333333 0.821604166666667 24 8.434 7.42139583333333 1.01260416666667 25 8.576 7.42139583333333 1.15460416666667 26 8.58 7.42139583333333 1.15860416666667 27 8.645 7.42139583333333 1.22360416666667 28 8.66 7.42139583333333 1.23860416666667 29 8.72 7.42139583333333 1.29860416666667 30 8.787 7.42139583333333 1.36560416666667 31 9.162 7.42139583333333 1.74060416666667 32 9.144 7.42139583333333 1.72260416666667 33 8.806 7.42139583333333 1.38460416666667 34 8.778 7.42139583333333 1.35660416666667 35 8.66 7.42139583333333 1.23860416666667 36 8.826 7.42139583333333 1.40460416666667 37 8.609 8.61041666666667 -0.00141666666666670 38 8.628 8.61041666666667 0.0175833333333334 39 8.619 8.61041666666667 0.00858333333333309 40 8.775 8.61041666666667 0.164583333333334 41 8.84 8.61041666666667 0.229583333333333 42 8.745 8.61041666666667 0.134583333333333 43 9.092 8.61041666666667 0.481583333333334 44 8.934 8.61041666666667 0.323583333333333 45 8.749 8.61041666666667 0.138583333333334 46 8.298 8.61041666666667 -0.312416666666667 47 8.067 8.61041666666667 -0.543416666666666 48 7.969 8.61041666666667 -0.641416666666666 49 7.999 7.42139583333333 0.577604166666666 50 7.865 7.42139583333333 0.443604166666667 51 7.746 7.42139583333333 0.324604166666667 52 7.633 7.42139583333333 0.211604166666667 53 7.458 7.42139583333333 0.036604166666667 54 7.391 7.42139583333333 -0.0303958333333332 55 7.856 7.42139583333333 0.434604166666667 56 7.72 7.42139583333333 0.298604166666667 57 7.297 7.42139583333333 -0.124395833333333 58 7.123 7.42139583333333 -0.298395833333333 59 7.004 7.42139583333333 -0.417395833333334 60 7.151 7.42139583333333 -0.270395833333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000729303320781405 0.00145860664156281 0.999270696679219 6 8.53225654734756e-05 0.000170645130946951 0.999914677434527 7 0.000861645675007357 0.00172329135001471 0.999138354324993 8 0.00110661166979544 0.00221322333959087 0.998893388330205 9 0.000348302233563704 0.000696604467127409 0.999651697766436 10 9.83775596114345e-05 0.000196755119222869 0.999901622440389 11 2.99110501428187e-05 5.98221002856375e-05 0.999970088949857 12 1.15244890995809e-05 2.30489781991619e-05 0.9999884755109 13 8.43667213359124e-06 1.68733442671825e-05 0.999991563327866 14 4.64397457909453e-06 9.28794915818906e-06 0.99999535602542 15 3.6542585501047e-06 7.3085171002094e-06 0.99999634574145 16 4.25735022231233e-06 8.51470044462466e-06 0.999995742649778 17 6.11560539018928e-06 1.22312107803786e-05 0.99999388439461 18 1.61278511562244e-05 3.22557023124489e-05 0.999983872148844 19 0.000747872707749601 0.00149574541549920 0.99925212729225 20 0.0316166566254352 0.0632333132508704 0.968383343374565 21 0.0952008123988537 0.190401624797707 0.904799187601146 22 0.477558487425137 0.955116974850274 0.522441512574863 23 0.735240826898629 0.529518346202743 0.264759173101371 24 0.885206239030858 0.229587521938284 0.114793760969142 25 0.952944940767146 0.0941101184657077 0.0470550592328538 26 0.977046901560787 0.0459061968784255 0.0229530984392128 27 0.988145000903007 0.0237099981939852 0.0118549990969926 28 0.993146950626806 0.0137060987463889 0.00685304937319445 29 0.996032154000747 0.0079356919985064 0.0039678459992532 30 0.997830608585478 0.00433878282904472 0.00216939141452236 31 0.999563629345024 0.000872741309951098 0.000436370654975549 32 0.999935834900397 0.000128330199206626 6.41650996033129e-05 33 0.999978352050581 4.32958988379212e-05 2.16479494189606e-05 34 0.999994514730915 1.09705381700253e-05 5.48526908501263e-06 35 0.999998690914848 2.61817030399621e-06 1.30908515199810e-06 36 0.99999997632519 4.73496198879978e-08 2.36748099439989e-08 37 0.99999991390036 1.72199279158234e-07 8.60996395791169e-08 38 0.999999698589645 6.02820710594317e-07 3.01410355297158e-07 39 0.999998982747625 2.03450475011009e-06 1.01725237505504e-06 40 0.999997019501984 5.96099603097202e-06 2.98049801548601e-06 41 0.999992542978382 1.49140432357085e-05 7.45702161785424e-06 42 0.99997990787919 4.01842416212849e-05 2.00921208106425e-05 43 0.999982630122758 3.47397544844124e-05 1.73698772422062e-05 44 0.999984553115666 3.08937686680909e-05 1.54468843340455e-05 45 0.99998562237372 2.87552525604619e-05 1.43776262802310e-05 46 0.99996078521554 7.84295689187456e-05 3.92147844593728e-05 47 0.999873534633512 0.000252930732975691 0.000126465366487845 48 0.999602679043015 0.00079464191396935 0.000397320956984675 49 0.999532770830448 0.000934458339104248 0.000467229169552124 50 0.999244107409245 0.00151178518151007 0.000755892590755034 51 0.998389058087396 0.00322188382520789 0.00161094191260395 52 0.99572738835588 0.00854522328823974 0.00427261164411987 53 0.986279509041728 0.0274409819165435 0.0137204909582718 54 0.958340768786372 0.0833184624272557 0.0416592312136279 55 0.954268124857746 0.0914637502845082 0.0457318751422541 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 39 0.764705882352941 NOK 5% type I error level 43 0.84313725490196 NOK 10% type I error level 47 0.92156862745098 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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