WS 7.5

*Unverified author*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 20 Nov 2009 10:20:37 -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/20/t1258737736c7adbqpqyqe4czs.htm/, Retrieved Fri, 20 Nov 2009 18:22:28 +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/2009/Nov/20/t1258737736c7adbqpqyqe4czs.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:

Dataseries X:

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9,3 7,5 9,8 9,9 8,3 6,8 9,3 9,8 8 6,5 8,3 9,3 8,5 6,6 8 8,3 10,4 7,6 8,5 8 11,1 8 10,4 8,5 10,9 8,1 11,1 10,4 10 7,7 10,9 11,1 9,2 7,5 10 10,9 9,2 7,6 9,2 10 9,5 7,8 9,2 9,2 9,6 7,8 9,5 9,2 9,5 7,8 9,6 9,5 9,1 7,5 9,5 9,6 8,9 7,5 9,1 9,5 9 7,1 8,9 9,1 10,1 7,5 9 8,9 10,3 7,5 10,1 9 10,2 7,6 10,3 10,1 9,6 7,7 10,2 10,3 9,2 7,7 9,6 10,2 9,3 7,9 9,2 9,6 9,4 8,1 9,3 9,2 9,4 8,2 9,4 9,3 9,2 8,2 9,4 9,4 9 8,2 9,2 9,4 9 7,9 9 9,2 9 7,3 9 9 9,8 6,9 9 9 10 6,6 9,8 9 9,8 6,7 10 9,8 9,3 6,9 9,8 10 9 7 9,3 9,8 9 7,1 9 9,3 9,1 7,2 9 9 9,1 7,1 9,1 9 9,1 6,9 9,1 9,1 9,2 7 9,1 9,1 8,8 6,8 9,2 9,1 8,3 6,4 8,8 9,2 8,4 6,7 8,3 8,8 8,1 6,6 8,4 8,3 7,7 6,4 8,1 8,4 7,9 6,3 7,7 8,1 7,9 6,2 7,9 7,7 8 6,5 7,9 7,9 7,9 6,8 8 7,9 7,6 6,8 7,9 8 7,1 6,4 7,6 7,9 6,8 6,1 7,1 7,6 6,5 5,8 6,8 7,1 6,9 6,1 6,5 6,8 8,2 7,2 6,9 6,5 8,7 7,3 8,2 6,9 8,3 6,9 8,7 8,2 7,9 6,1 8,3 8,7 7,5 5,8 7,9 8,3 7,8 6,2 7,5 7,9

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 WLMan[t] = + 3.65718934610865 + 0.395497505499312WLVrouw[t] + 0.191002977382953`Yt-1`[t] -0.138059867944866`Yt-2`[t] -0.099406851289696M1[t] -0.148951401377357M2[t] -0.234467327975613M3[t] -0.471178750524076M4[t] -0.448031656398712M5[t] -0.708998951622607M6[t] -0.565548945759982M7[t] -0.499274537665341M8[t] -0.394140575303057M9[t] -0.195156370453495M10[t] -0.0142767368236248M11[t] -0.00669916588971114t + 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) 3.65718934610865 1.264152 2.893 0.006024 0.003012 WLVrouw 0.395497505499312 0.254641 1.5532 0.12789 0.063945 `Yt-1` 0.191002977382953 0.406998 0.4693 0.641285 0.320642 `Yt-2` -0.138059867944866 0.255103 -0.5412 0.591235 0.295617 M1 -0.099406851289696 0.278415 -0.357 0.722845 0.361422 M2 -0.148951401377357 0.285278 -0.5221 0.604325 0.302163 M3 -0.234467327975613 0.290255 -0.8078 0.423759 0.21188 M4 -0.471178750524076 0.292672 -1.6099 0.114906 0.057453 M5 -0.448031656398712 0.366738 -1.2217 0.228647 0.114323 M6 -0.708998951622607 0.32784 -2.1626 0.036311 0.018156 M7 -0.565548945759982 0.285832 -1.9786 0.054443 0.027222 M8 -0.499274537665341 0.290653 -1.7178 0.093205 0.046602 M9 -0.394140575303057 0.29421 -1.3397 0.18756 0.09378 M10 -0.195156370453495 0.306503 -0.6367 0.527763 0.263882 M11 -0.0142767368236248 0.292262 -0.0488 0.961271 0.480636 t -0.00669916588971114 0.006096 -1.099 0.278048 0.139024 Multiple Linear Regression - Regression Statistics Multiple R 0.844394446216218 R-squared 0.713001980800794 Adjusted R-squared 0.610502688229648 F-TEST (value) 6.95616489553717 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 3.1064643501999e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.409325621372292 Sum Squared Residuals 7.03699350109613 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.5 7.73424661577162 -0.234246615771617 2 6.8 7.20080989239794 -0.400809892397944 3 6.5 6.86797250484966 -0.367972504849663 4 6.6 6.90306964389112 -0.303069643891124 5 7.6 7.8078822816504 -0.207882281650406 6 8 8.1109397974415 -0.110939797441497 7 8.1 8.03997947138737 0.0600205286126291 8 7.7 7.60876445560492 0.0912355443950769 9 7.5 7.24651054162236 0.253489458377639 10 7.6 7.41024707982623 0.189752920173772 11 7.8 7.81352469357208 -0.0135246935720755 12 7.8 7.9179529082708 -0.117952908270805 13 7.8 7.7499794778963 0.0500205221036976 14 7.5 7.50263047518642 -0.00263047518642345 15 7.5 7.2687206774399 0.231279322560101 16 7.1 7.08188319125301 0.0181168087469879 17 7.5 7.58009064686518 -0.080090646865176 18 7.5 7.5878209751782 -0.0878209751781949 19 7.6 7.57135680533842 0.0286431946615845 20 7.7 7.34692127291649 0.353078727083511 21 7.7 7.18636126755405 0.513638732445948 22 7.9 7.42463078687757 0.475369213122428 23 8.1 7.7126852500839 0.387314749916095 24 8.2 7.72555713196163 0.474442868038372 25 8.2 7.52654562688787 0.673454373112129 26 8.2 7.35300181433405 0.846998185665954 27 7.9 7.25019809995846 0.649801900041539 28 7.3 7.03439948510926 0.265600514890740 29 6.9 7.36724541774436 -0.467245417744362 30 6.6 7.33148083963698 -0.731480839636982 31 6.7 7.31688487963073 -0.61688487963073 32 6.9 7.11289880002044 -0.212898800020441 33 7 7.02479482974072 -0.0247948297407169 34 7.1 7.22880890945811 -0.128808909458114 35 7.2 7.48395708813166 -0.283957088131664 36 7.1 7.51063495680387 -0.410634956803873 37 6.9 7.39072295282998 -0.490722952829979 38 7 7.37402898740254 -0.374028987402538 39 6.8 7.14271519045314 -0.342715190453143 40 6.4 6.61134867151764 -0.211348671517644 41 6.7 6.6270688087897 0.0729311912103026 42 6.6 6.32888332773703 0.271116672262974 43 6.4 6.23632828550084 0.163671714499158 44 6.3 6.34001979823591 -0.0400197982359138 45 6.2 6.53187913736302 -0.331879137363024 46 6.5 6.73610195328383 -0.236101953283832 47 6.8 6.88983296821236 -0.0898329682123556 48 6.8 6.74585500296369 0.0541449970363064 49 6.4 6.39850532661423 0.00149467338576981 50 6.1 6.16952883067905 -0.0695288306790485 51 5.8 5.97039352729883 -0.170393527298835 52 6.1 5.86929900822896 0.230700991771041 53 7.2 6.51771284495036 0.682287155049642 54 7.3 6.6408750600063 0.659124939993699 55 6.9 6.53545055814264 0.364549441857359 56 6.1 6.29139567322223 -0.191395673222233 57 5.8 6.21045422371985 -0.410454223719846 58 6.2 6.50021127055425 -0.300211270554254 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.00203712757715894 0.00407425515431788 0.99796287242284 20 0.000193269212546471 0.000386538425092942 0.999806730787454 21 3.23686810988154e-05 6.47373621976308e-05 0.999967631318901 22 6.40359514837804e-06 1.28071902967561e-05 0.999993596404852 23 2.85492669698133e-06 5.70985339396266e-06 0.999997145073303 24 0.000141514788643273 0.000283029577286546 0.999858485211357 25 0.000476534041134436 0.000953068082268871 0.999523465958866 26 0.00379999030208807 0.00759998060417615 0.996200009697912 27 0.00932078254622554 0.0186415650924511 0.990679217453774 28 0.00751343079785643 0.0150268615957129 0.992486569202144 29 0.0367458405798868 0.0734916811597736 0.963254159420113 30 0.434397536781352 0.868795073562704 0.565602463218648 31 0.804040814449024 0.391918371101953 0.195959185550976 32 0.782367246478276 0.435265507043448 0.217632753521724 33 0.976501149066028 0.0469977018679448 0.0234988509339724 34 0.997460403594263 0.00507919281147393 0.00253959640573697 35 0.995399982953186 0.00920003409362781 0.00460001704681391 36 0.995166709872065 0.00966658025587057 0.00483329012793528 37 0.9985213113519 0.00295737729620157 0.00147868864810078 38 0.998926683991556 0.00214663201688754 0.00107331600844377 39 0.994611337200477 0.0107773255990460 0.00538866279952299 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.619047619047619 NOK 5% type I error level 17 0.80952380952381 NOK 10% type I error level 18 0.857142857142857 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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