Mutiple Regression (c)

*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, 19 Nov 2009 10:02:17 -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/19/t125865020879aerp8g95r0bbc.htm/, Retrieved Thu, 19 Nov 2009 18:03:39 +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/19/t125865020879aerp8g95r0bbc.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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4 7.2 102.9 271244 4.1 7.4 97.4 269907 4 8.8 111.4 271296 3.8 9.3 87.4 270157 4.7 9.3 96.8 271322 4.3 8.7 114.1 267179 3.9 8.2 110.3 264101 4 8.3 103.9 265518 4.3 8.5 101.6 269419 4.8 8.6 94.6 268714 4.4 8.5 95.9 272482 4.3 8.2 104.7 268351 4.7 8.1 102.8 268175 4.7 7.9 98.1 270674 4.9 8.6 113.9 272764 5 8.7 80.9 272599 4.2 8.7 95.7 270333 4.3 8.5 113.2 270846 4.8 8.4 105.9 270491 4.8 8.5 108.8 269160 4.8 8.7 102.3 274027 4.2 8.7 99 273784 4.6 8.6 100.7 276663 4.8 8.5 115.5 274525 4.5 8.3 100.7 271344 4.4 8 109.9 271115 4.3 8.2 114.6 270798 3.9 8.1 85.4 273911 3.7 8.1 100.5 273985 4 8 114.8 271917 4.1 7.9 116.5 273338 3.7 7.9 112.9 270601 3.8 8 102 273547 3.8 8 106 275363 3.8 7.9 105.3 281229 3.3 8 118.8 277793 3.3 7.7 106.1 279913 3.3 7.2 109.3 282500 3.2 7.5 117.2 280041 3.4 7.3 92.5 282166 4.2 7 104.2 290304 4.9 7 112.5 283519 5.1 7 122.4 287816 5.5 7.2 113.3 285226 5.6 7.3 100 287595 6.4 7.1 110.7 289741 6.1 6.8 112.8 289148 7.1 6.4 109.8 288301 7.8 6.1 117.3 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Cons.index[t] = + 19.8323313000439 -1.11527239893313Werkl.graad[t] + 0.0592692204393098Industr.prod.[t] -4.72987636397039e-05BrutoSchuld[t] -0.138329455861971M1[t] -0.174984360839047M2[t] + 0.118530643566972M3[t] + 1.72276445087934M4[t] + 1.08257251377214M5[t] -0.183897004637514M6[t] -0.365649427478667M7[t] + 0.0349713938371719M8[t] + 1.10057063459926M9[t] + 1.07419310706961M10[t] + 0.88624753907484M11[t] + 0.00239849032578529t + 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) 19.8323313000439 11.550665 1.717 0.092297 0.046149 Werkl.graad -1.11527239893313 0.381758 -2.9214 0.005257 0.002628 Industr.prod. 0.0592692204393098 0.04285 1.3832 0.172877 0.086439 BrutoSchuld -4.72987636397039e-05 2.6e-05 -1.7963 0.078618 0.039309 M1 -0.138329455861971 0.836173 -0.1654 0.869285 0.434642 M2 -0.174984360839047 0.863123 -0.2027 0.840182 0.420091 M3 0.118530643566972 0.780211 0.1519 0.879873 0.439936 M4 1.72276445087934 1.190997 1.4465 0.154407 0.077204 M5 1.08257251377214 0.89427 1.2106 0.231869 0.115934 M6 -0.183897004637514 0.804561 -0.2286 0.820156 0.410078 M7 -0.365649427478667 0.804502 -0.4545 0.651473 0.325737 M8 0.0349713938371719 0.814636 0.0429 0.965933 0.482966 M9 1.10057063459926 0.884905 1.2437 0.219521 0.109761 M10 1.07419310706961 0.875003 1.2276 0.225445 0.112723 M11 0.88624753907484 0.852007 1.0402 0.303358 0.151679 t 0.00239849032578529 0.025387 0.0945 0.925116 0.462558 Multiple Linear Regression - Regression Statistics Multiple R 0.701043436297933 R-squared 0.491461899576414 Adjusted R-squared 0.335786970875316 F-TEST (value) 3.15697526683979 F-TEST (DF numerator) 15 F-TEST (DF denominator) 49 p-value 0.00119475423289339 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.25215829746234 Sum Squared Residuals 76.8271196932854 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.9357360007064 -0.9357360007064 2 4.1 4.41568284083848 -0.315682840838480 3 4 3.91428608051869 0.0857139194813111 4 3.8 3.59469417993247 0.205305820067534 5 4.7 3.45892834564031 1.24107165435969 6 4.3 4.08533704827567 0.214662951724329 7 3.9 4.3839818720405 -0.483981872040501 8 4 4.22912858489977 -0.229128584899767 9 4.3 4.75324015223212 -0.453240152232118 10 4.8 4.23619496042576 0.563805039574235 11 4.4 4.06100336782679 0.338996632173208 12 4.3 4.22869637121922 0.0713036287807819 13 4.7 4.10000570914224 0.599994290857756 14 4.7 3.8920388278772 0.8079611721228 15 4.9 4.24486091028993 0.65513908971007 16 5 3.7918859895381 1.2081140104619 17 4.2 4.13845600366604 0.0615439963339579 18 4.3 4.11038654730955 0.189613452690452 19 4.8 3.62668560657263 1.17331439342737 20 4.8 4.15301307199938 0.646986928000618 21 4.8 4.38250330781068 0.417496692189324 22 4.2 4.17442944272154 0.0255705572784602 23 4.6 4.06499413917399 0.535005860826013 24 4.8 4.27098154948172 0.529018450518284 25 4.5 3.63137796836827 0.868622031631732 26 4.4 4.48781151831206 -0.0878115183120578 27 4.3 4.85422957739578 -0.55422957739578 28 3.9 4.694486826889 -0.794486826889002 29 3.7 4.94815850023183 -1.24815850023183 30 4 4.74097840753031 -0.740978407530308 31 4.1 4.70669784652306 -0.60669784652306 32 3.7 5.02580468066504 -1.32580468066504 33 3.8 5.19689851138855 -1.39689851138855 34 3.8 5.32410180117223 -1.52410180117223 35 3.8 4.93113896157854 -1.13113896157854 36 3.3 4.89841570073287 -1.59841570073287 37 3.3 4.24407397638122 -0.94407397638122 38 3.3 4.83475336506637 -1.53475336506637 39 3.2 5.38061964137882 -2.18061964137882 40 3.4 5.64584680121827 -2.24584680121827 41 4.2 5.65116761475681 -1.45116761475681 42 4.9 5.1999532276146 -0.299953227614603 43 5.1 5.4041217900886 -0.304121790088595 44 5.5 5.16724051377271 0.332759486227293 45 5.6 5.22337960206199 0.376620397938012 46 6.4 5.95513255657456 0.444867443425439 47 6.1 6.25668072834641 -0.156680728346411 48 7.1 5.68119503065551 1.41880496934449 49 7.8 6.23667303030607 1.56332696969393 50 7.9 5.29428052164452 2.60571947835548 51 7.4 4.72220397730317 2.67779602269683 52 7.5 4.87306590055413 2.62693409944587 53 6.8 4.65194790757918 2.14805209242082 54 5.2 4.56334476926987 0.63665523073013 55 4.7 4.47851288477522 0.221487115224784 56 4.1 3.52481314866310 0.575186851336896 57 3.9 2.84397842650666 1.05602157349334 58 2.6 2.11014123910591 0.489858760894095 59 2.7 2.28618280307427 0.413817196925726 60 1.8 2.22071134791069 -0.420711347910689 61 1 2.15213331509580 -1.15213331509580 62 0.3 1.77543292626138 -1.47543292626138 63 1.3 1.98379981311361 -0.683799813113611 64 1 2.00002030186803 -1.00002030186803 65 1.1 1.85134162812582 -0.751341628125817 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0543027612910795 0.108605522582159 0.94569723870892 20 0.0179286040309618 0.0358572080619237 0.982071395969038 21 0.00545734643511248 0.0109146928702250 0.994542653564888 22 0.00463566625863346 0.00927133251726693 0.995364333741366 23 0.00168912832245157 0.00337825664490313 0.998310871677548 24 0.000914553265246275 0.00182910653049255 0.999085446734754 25 0.00104599789260711 0.00209199578521422 0.998954002107393 26 0.000483012102548328 0.000966024205096656 0.999516987897452 27 0.000244621936788949 0.000489243873577899 0.999755378063211 28 0.000269834089363532 0.000539668178727065 0.999730165910636 29 0.000203284995945337 0.000406569991890673 0.999796715004055 30 9.89555330327366e-05 0.000197911066065473 0.999901044466967 31 5.68724174583902e-05 0.000113744834916780 0.999943127582542 32 2.39610085981348e-05 4.79220171962695e-05 0.999976038991402 33 1.63973109905682e-05 3.27946219811365e-05 0.99998360268901 34 6.99255884753423e-06 1.39851176950685e-05 0.999993007441152 35 3.33821857068115e-06 6.6764371413623e-06 0.99999666178143 36 6.36122086135732e-06 1.27224417227146e-05 0.999993638779139 37 1.72072569962733e-05 3.44145139925466e-05 0.999982792743004 38 6.43323019798005e-06 1.28664603959601e-05 0.999993566769802 39 3.12367154777209e-06 6.24734309554418e-06 0.999996876328452 40 2.06149163271832e-06 4.12298326543664e-06 0.999997938508367 41 4.55151393175996e-06 9.10302786351992e-06 0.999995448486068 42 3.87491782247308e-06 7.74983564494616e-06 0.999996125082178 43 6.44263486316505e-06 1.28852697263301e-05 0.999993557365137 44 6.90061738930881e-05 0.000138012347786176 0.999930993826107 45 0.00357598749966047 0.00715197499932094 0.99642401250034 46 0.0158633224177949 0.0317266448355898 0.984136677582205 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.857142857142857 NOK 5% type I error level 27 0.964285714285714 NOK 10% type I error level 27 0.964285714285714 NOK

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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