*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, 02 Dec 2010 22:34:45 +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/02/t1291329258ug6da18n74pg9w8.htm/, Retrieved Thu, 02 Dec 2010 23:34:28 +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/02/t1291329258ug6da18n74pg9w8.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:

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603.6 0 741.7 993.3 -820.8 -145.8 0 603.6 741.7 993.3 -35.1 0 -145.8 603.6 741.7 395.1 0 -35.1 -145.8 603.6 523.1 0 395.1 -35.1 -145.8 462.3 0 523.1 395.1 -35.1 183.4 0 462.3 523.1 395.1 791.5 0 183.4 462.3 523.1 344.8 0 791.5 183.4 462.3 -217.0 0 344.8 791.5 183.4 406.7 0 -217.0 344.8 791.5 228.6 0 406.7 -217.0 344.8 -580.1 0 228.6 406.7 -217.0 -1550.4 0 -580.1 228.6 406.7 -1447.5 0 -1550.4 -580.1 228.6 -40.1 0 -1447.5 -1550.4 -580.1 -1033.5 0 -40.1 -1447.5 -1550.4 -925.6 0 -1033.5 -40.1 -1447.5 -347.8 0 -925.6 -1033.5 -40.1 -447.7 0 -347.8 -925.6 -1033.5 -102.6 0 -447.7 -347.8 -925.6 -2062.2 0 -102.6 -447.7 -347.8 -929.7 1 -2062.2 -102.6 -447.7 -720.7 1 -929.7 -2062.2 -102.6 -1541.8 1 -720.7 -929.7 -2062.2 -1432.3 1 -1541.8 -720.7 -929.7 -1216.2 1 -1432.3 -1541.8 -720.7 -212.8 1 -1216.2 -1432.3 -1541.8 -378.2 1 -212.8 -1216.2 -1432.3 76.9 1 -378.2 -212.8 -1216.2 -101.3 1 76.9 -378.2 -212.8 220.4 1 -101.3 76.9 -378.2 495.6 1 220.4 -101.3 76.9 -1035.2 1 495.6 220.4 -101.3 61. etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Totaal[t] = -12.6450584188877 + 275.169286301869Dummy[t] + 0.29523736946469vertraging1[t] + 0.456063770979032vertraging2[t] + 0.149937295128415vertraging3[t] -322.735387706527M1[t] -968.227700030195M2[t] -453.002567742199M3[t] + 722.890840676447M4[t] + 343.955904339616M5[t] -216.469081464292M6[t] -28.0228331351933M7[t] + 394.064402937318M8[t] + 309.907158270251M9[t] -1185.56832625582M10[t] + 166.465422769620M11[t] -2.80813744948333t + 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) -12.6450584188877 344.360516 -0.0367 0.970951 0.485476 Dummy 275.169286301869 281.792039 0.9765 0.336627 0.168313 vertraging1 0.29523736946469 0.183224 1.6113 0.117577 0.058788 vertraging2 0.456063770979032 0.173782 2.6243 0.013523 0.006762 vertraging3 0.149937295128415 0.183595 0.8167 0.420552 0.210276 M1 -322.735387706527 498.772024 -0.6471 0.522514 0.261257 M2 -968.227700030195 389.349342 -2.4868 0.01868 0.00934 M3 -453.002567742199 415.49054 -1.0903 0.284268 0.142134 M4 722.890840676447 367.378619 1.9677 0.058408 0.029204 M5 343.955904339616 433.583111 0.7933 0.43384 0.21692 M6 -216.469081464292 472.947964 -0.4577 0.650465 0.325232 M7 -28.0228331351933 395.255413 -0.0709 0.943949 0.471975 M8 394.064402937318 386.521762 1.0195 0.316111 0.158055 M9 309.907158270251 420.322843 0.7373 0.466663 0.233332 M10 -1185.56832625582 438.541996 -2.7034 0.011192 0.005596 M11 166.465422769620 478.106533 0.3482 0.730139 0.36507 t -2.80813744948333 10.561076 -0.2659 0.792139 0.396069 Multiple Linear Regression - Regression Statistics Multiple R 0.86614625861463 R-squared 0.750209341312121 Adjusted R-squared 0.616987656678586 F-TEST (value) 5.63128550262511 F-TEST (DF numerator) 16 F-TEST (DF denominator) 30 p-value 2.44282330922330e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 441.620383129706 Sum Squared Residuals 5850856.88386886 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 603.6 210.728585229132 392.871414770868 2 -145.8 -321.088542952958 175.288542952958 3 -35.1 -130.629063017799 95.5290630177994 4 395.1 712.658454322183 -317.558454322183 5 523.1 396.049747357724 127.050252642276 6 462.3 83.4037002417086 378.896299758291 7 183.4 373.97056610743 -190.57056610743 8 791.5 702.371258887669 89.1287411123312 9 344.8 658.627347872737 -313.827347872737 10 -217 -736.023939521666 519.023939521666 11 406.7 334.790500560289 71.9094994397113 12 228.6 26.4628714064295 202.137128593571 13 -580.1 -151.450227694763 -428.649772305237 14 -1550.4 -1026.21820479378 -524.181795206217 15 -1447.5 -1195.79263339997 -251.707366600028 16 -40.1 -556.100404664197 516.000404664197 17 -1033.5 -620.881600095266 -412.618399904734 18 -925.6 -820.110827230277 -105.489172769724 19 -347.8 -844.64860511226 496.84860511226 20 -447.7 -354.519782504464 -93.1802174955358 21 -102.6 -191.287496814496 88.687496814496 22 -2062.2 -1546.6117041834 -515.588295816601 23 -929.7 -358.355083927040 -571.34491607296 24 -720.7 -1035.23152828908 314.531528289077 25 -1541.8 -1076.39534612685 -465.404653873146 26 -1432.3 -1701.99388509992 269.693885099915 27 -1216.2 -1500.38546597406 284.185465974064 28 -212.8 -336.673929571319 123.873929571319 29 -378.2 -307.202312111633 -70.9976878883672 30 76.9 -429.251858996873 506.151858996873 31 -101.3 -34.2370870619575 -67.0629129380425 32 220.4 515.185705880781 -294.785705880781 33 495.6 510.164084545499 -14.5640845454994 34 -1035.2 -786.873324221307 -248.326675778693 35 61.8 284.146499794348 -222.346499794348 36 -734.8 -218.131343117353 -516.668656882647 37 -6.9 -508.083011407514 501.183011407514 38 -1061.1 -1140.29936715334 79.1993671533435 39 -854.6 -726.592837608164 -128.007162391836 40 -186.5 135.815879913334 -322.315879913334 41 244 -112.565835150826 356.565835150826 42 -992.6 -213.041014014559 -779.55898598544 43 -335.2 -95.9848739332123 -239.215126066788 44 316.8 17.9628177360146 298.837182263985 45 477.6 237.896064396260 239.703935603740 46 -572.1 -816.991032073629 244.891032073629 47 1115.2 393.418083572403 721.781916427597 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.206136929331396 0.412273858662792 0.793863070668604 21 0.284601927083196 0.569203854166392 0.715398072916804 22 0.194719603072802 0.389439206145604 0.805280396927198 23 0.150665223491057 0.301330446982114 0.849334776508943 24 0.0855073624281634 0.171014724856327 0.914492637571837 25 0.128516501358591 0.257033002717182 0.871483498641409 26 0.180062852306123 0.360125704612245 0.819937147693877 27 0.144535848798010 0.289071697596021 0.85546415120199 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 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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Software written by Ed van Stee & Patrick Wessa

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