*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: Tue, 24 Nov 2009 01:40:29 -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/24/t1259052091ppd6k4lcrltk02z.htm/, Retrieved Tue, 24 Nov 2009 09:41:43 +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/24/t1259052091ppd6k4lcrltk02z.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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267413 294912 267366 293488 264777 290555 258863 284736 254844 281818 254868 287854 277267 316263 285351 325412 286602 326011 283042 328282 276687 317480 277915 317539 277128 313737 277103 312276 275037 309391 270150 302950 267140 300316 264993 304035 287259 333476 291186 337698 292300 335932 288186 323931 281477 313927 282656 314485 280190 313218 280408 309664 276836 302963 275216 298989 274352 298423 271311 301631 289802 329765 290726 335083 292300 327616 278506 309119 269826 295916 265861 291413 269034 291542 264176 284678 255198 276475 253353 272566 246057 264981 235372 263290 258556 296806 260993 303598 254663 286994 250643 276427 243422 266424 247105 267153 248541 268381 245039 262522 237080 255542 237085 253158 225554 243803 226839 250741 247934 280445 248333 285257 246969 270976 245098 261076 246263 255603 255765 260376 264319 263903 268347 264291 273046 263276 273963 262572 267430 256167 271993 264221 292710 293860

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 93124.3064063537 + 0.595245145625902X[t] + 1460.64625979357M1[t] + 2625.50165379033M2[t] + 2063.61079494683M3[t] + 2144.30079128605M4[t] -474.914587784631M5[t] -4747.33433857108M6[t] -1131.23893509993M7[t] -6743.02998141279M8[t] -2789.33139941479M9[t] -2464.15797519326M10[t] -2133.01676893371M11[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) 93124.3064063537 16338.164757 5.6998 1e-06 0 X 0.595245145625902 0.054336 10.955 0 0 M1 1460.64625979357 5794.131653 0.2521 0.801928 0.400964 M2 2625.50165379033 5795.421135 0.453 0.652342 0.326171 M3 2063.61079494683 5807.031147 0.3554 0.723701 0.361851 M4 2144.30079128605 5824.907886 0.3681 0.714218 0.357109 M5 -474.914587784631 5858.378469 -0.0811 0.935689 0.467845 M6 -4747.33433857108 5827.960201 -0.8146 0.418891 0.209446 M7 -1131.23893509993 5878.16325 -0.1924 0.848113 0.424057 M8 -6743.02998141279 6229.689339 -1.0824 0.283884 0.141942 M9 -2789.33139941479 6141.928098 -0.4541 0.651544 0.325772 M10 -2464.15797519326 6073.938233 -0.4057 0.686571 0.343285 M11 -2133.01676893371 6051.646679 -0.3525 0.725859 0.362929 Multiple Linear Regression - Regression Statistics Multiple R 0.860025172821497 R-squared 0.739643297886646 Adjusted R-squared 0.681786252972568 F-TEST (value) 12.7839798763498 F-TEST (DF numerator) 12 F-TEST (DF denominator) 54 p-value 7.89301957127009e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9568.45326181193 Sum Squared Residuals 4943986082.46788 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 267413 270129.889052973 -2716.88905297294 2 267366 270447.115359599 -3081.11535959852 3 264777 268139.370488634 -3362.37048863429 4 258863 264756.328982576 -5893.32898257637 5 254844 260400.188268569 -5556.18826856933 6 254868 259720.668216781 -4852.66821678082 7 277267 280247.082962338 -2980.08296233820 8 285351 280081.189753357 5269.81024664329 9 286602 284391.440177585 2210.55982241537 10 283042 286068.415327523 -3026.41532752258 11 276687 279969.718470731 -3282.71847073114 12 277915 282137.854703257 -4222.85470325678 13 277128 281335.378919381 -4207.37891938067 14 277103 281630.581155618 -4527.58115561799 15 275037 279351.408051644 -4314.40805164376 16 270150 275598.124065007 -5448.12406500655 17 267140 271411.032972357 -4271.03297235725 18 264993 269352.329918154 -4359.32991815353 19 287259 290493.037653997 -3234.03765399685 20 291186 287394.371612517 3791.62838748346 21 292300 290296.867267339 2003.1327326608 22 288186 283478.503698904 4707.49630109572 23 281477 277854.812468322 3622.18753167769 24 282656 280319.976028515 2336.02397148472 25 280190 281026.446688801 -836.446688800826 26 280408 280075.800835243 332.199164756861 27 276836 275525.172255560 1310.82774443953 28 275216 273240.358043182 1975.64195681765 29 274352 270284.233911687 4067.76608831259 30 271311 267921.360588069 3389.63941193114 31 289802 288284.082918579 1517.91708142087 32 290726 285837.805556705 4888.19444329519 33 292300 285346.808636314 6953.1913636858 34 278506 274661.732601893 3844.26739810657 35 269826 267133.852150454 2692.1478495458 36 265861 266586.480028634 -725.480028634476 37 269034 268123.912912214 910.087087786215 38 264176 265203.005626634 -1027.00562663437 39 255198 259758.318838222 -4560.31883822159 40 253353 257512.195560309 -4159.19556030916 41 246057 250378.045751666 -4321.04575166602 42 235372 245099.066459626 -9727.06645962618 43 258556 268665.398163895 -10109.3981638950 44 260993 267096.512146673 -6103.5121466733 45 254663 261166.760330699 -6503.76033069883 46 250643 255201.978301091 -4558.97830109146 47 243422 249578.882315655 -6156.88231565511 48 247105 252145.83279575 -5040.8327957501 49 248541 254337.440094372 -5796.44009437228 50 245039 252014.754180147 -6975.75418014688 51 237080 247298.052204835 -10218.0522048346 52 237085 245959.677774002 -8874.67777400166 53 225554 237771.944057601 -12217.9440576007 54 226839 237629.335127167 -10790.3351271667 55 247934 258926.592336310 -10992.5923363097 56 248333 256179.120930749 -7846.12093074864 57 246969 251632.123588063 -4663.12358806314 58 245098 246064.370070588 -966.370070588245 59 246263 243137.734594837 3125.26540516277 60 255765 248111.856443843 7653.14355615663 61 264319 251671.932332259 12647.0676677405 62 268347 253067.742842759 15279.2571572409 63 273046 251901.678161105 21144.3218388947 64 273963 251563.315574924 22399.6844250761 65 267430 245131.555038119 22298.4449618807 66 271993 245653.239690204 26339.7603097961 67 292710 266911.805964881 25798.1940351189 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000272740306682288 0.000545480613364576 0.999727259693318 17 8.40239482044959e-05 0.000168047896408992 0.999915976051795 18 7.49170597548235e-06 1.49834119509647e-05 0.999992508294025 19 4.92950080567018e-07 9.85900161134036e-07 0.99999950704992 20 5.98715748209359e-08 1.19743149641872e-07 0.999999940128425 21 3.62299972378704e-09 7.24599944757409e-09 0.999999996377 22 2.10110891749833e-06 4.20221783499666e-06 0.999997898891082 23 3.95714747858896e-06 7.91429495717792e-06 0.999996042852521 24 3.70853660413269e-06 7.41707320826538e-06 0.999996291463396 25 1.19816370468405e-06 2.39632740936809e-06 0.999998801836295 26 5.85719310664065e-07 1.17143862132813e-06 0.99999941428069 27 3.79400249429956e-07 7.58800498859913e-07 0.99999962059975 28 6.51165243118333e-07 1.30233048623667e-06 0.999999348834757 29 1.29136350023109e-06 2.58272700046217e-06 0.9999987086365 30 1.29952461265898e-06 2.59904922531795e-06 0.999998700475387 31 5.39656413898947e-07 1.07931282779789e-06 0.999999460343586 32 1.45978497106152e-07 2.91956994212303e-07 0.999999854021503 33 6.76760033735602e-08 1.35352006747120e-07 0.999999932323997 34 2.27338012034522e-08 4.54676024069044e-08 0.999999977266199 35 6.51820861675371e-09 1.30364172335074e-08 0.999999993481791 36 1.53816005183794e-09 3.07632010367588e-09 0.99999999846184 37 4.89495386889852e-10 9.78990773779704e-10 0.999999999510505 38 1.24912743062200e-10 2.49825486124401e-10 0.999999999875087 39 4.88148937542593e-11 9.76297875085186e-11 0.999999999951185 40 1.89791477030563e-11 3.79582954061126e-11 0.99999999998102 41 9.34239246869916e-12 1.86847849373983e-11 0.999999999990658 42 2.21511899107560e-11 4.43023798215119e-11 0.999999999977849 43 1.08375414951116e-10 2.16750829902233e-10 0.999999999891625 44 2.56484865842372e-10 5.12969731684744e-10 0.999999999743515 45 4.75735421326044e-10 9.51470842652088e-10 0.999999999524265 46 2.34334157908895e-09 4.68668315817789e-09 0.999999997656658 47 7.47462107226761e-08 1.49492421445352e-07 0.99999992525379 48 5.70879206197699e-06 1.14175841239540e-05 0.999994291207938 49 0.0181150133568992 0.0362300267137984 0.9818849866431 50 0.382683330595654 0.765366661191308 0.617316669404346 51 0.798556772882816 0.402886454234369 0.201443227117184 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 33 0.916666666666667 NOK 5% type I error level 34 0.944444444444444 NOK 10% type I error level 34 0.944444444444444 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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