SHw WS7

*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: Wed, 18 Nov 2009 11:21:38 -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/18/t12585686045ffna0wkavad4b7.htm/, Retrieved Wed, 18 Nov 2009 19:23:36 +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/18/t12585686045ffna0wkavad4b7.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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627 356 696 386 825 444 677 387 656 327 785 448 412 225 352 182 839 460 729 411 696 342 641 361 695 377 638 331 762 428 635 340 721 352 854 461 418 221 367 198 824 422 687 329 601 320 676 375 740 364 691 351 683 380 594 319 729 322 731 386 386 221 331 187 707 344 715 342 657 365 653 313 642 356 643 337 718 389 654 326 632 343 731 357 392 220 344 228 792 391 852 425 649 332 629 298 685 360 617 326 715 325 715 393 629 301 916 426 531 265 357 210 917 429 828 440 708 357 858 431

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 Y[t] = + 186.680604490460 + 1.33076756412887X[t] -13.2908466500560M1[t] -13.1412155346012M2[t] + 7.03775201508341M3[t] -25.940348843195M4[t] + 23.5231157596390M5[t] + 37.4036877698205M6[t] -92.6131162897724M7[t] -131.963506840643M8[t] + 55.695729371469M9[t] + 27.5699702049618M10[t] -11.8235252685434M11[t] + 0.87495693625875t + 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) 186.680604490460 58.68401 3.1811 0.002628 0.001314 X 1.33076756412887 0.152821 8.708 0 0 M1 -13.2908466500560 23.460541 -0.5665 0.573795 0.286897 M2 -13.1412155346012 23.478299 -0.5597 0.578388 0.289194 M3 7.03775201508341 24.014546 0.2931 0.770793 0.385396 M4 -25.940348843195 23.362433 -1.1103 0.272621 0.136311 M5 23.5231157596390 23.717236 0.9918 0.326476 0.163238 M6 37.4036877698205 24.979963 1.4973 0.141134 0.070567 M7 -92.6131162897724 30.236008 -3.063 0.003656 0.001828 M8 -131.963506840643 33.249812 -3.9688 0.000251 0.000126 M9 55.695729371469 24.631659 2.2611 0.028524 0.014262 M10 27.5699702049618 23.80686 1.1581 0.252814 0.126407 M11 -11.8235252685434 23.327587 -0.5068 0.614683 0.307342 t 0.87495693625875 0.28123 3.1112 0.003198 0.001599 Multiple Linear Regression - Regression Statistics Multiple R 0.974557674504662 R-squared 0.949762660935936 Adjusted R-squared 0.935565152070004 F-TEST (value) 66.8964302050912 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36.7556804677554 Sum Squared Residuals 62145.082145796 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 627 648.01796760654 -21.0179676065400 2 696 688.965582582119 7.03441741788135 3 825 787.204025787536 37.7959742124637 4 677 679.247130710171 -2.24713071017142 5 656 649.739498401532 6.26050159846768 6 785 825.517902607565 -40.5179026075653 7 412 399.614888683494 12.3851113165059 8 352 303.916449811342 48.0835501886583 9 839 862.404025787536 -23.4040257875364 10 729 769.945612914973 -40.9456129149735 11 696 639.604112452835 56.3958875471646 12 641 677.587178376086 -36.5871783760859 13 695 686.46356968835 8.53643031164946 14 638 626.272849790136 11.7271502098637 15 762 776.41122799658 -14.4112279965795 16 635 627.20053843122 7.79946156878024 17 721 693.508170739859 27.4918292601411 18 854 853.317364176345 0.682635823654558 19 418 404.791301662084 13.2086983379163 20 367 335.708214072508 31.2917859274916 21 824 822.334341585744 1.66565841425553 22 687 671.322155891512 15.6778441084884 23 601 620.826709277105 -19.8267092771054 24 676 706.717407508995 -30.717407508995 25 740 679.66307458978 60.3369254102197 26 691 663.387684307819 27.6123156921814 27 683 723.033868153499 -40.033868153499 28 594 609.753902819619 -15.7539028196186 29 729 664.084627051098 64.915372948902 30 731 764.009280101786 -33.0092801017856 31 386 415.290784897189 -29.2907848971887 32 331 331.569254102196 -0.569254102195894 33 707 729.033954818798 -22.0339548187980 34 715 699.121617460292 15.8783825397082 35 657 691.210732898009 -34.2107328980093 36 653 634.70930176811 18.2906982318896 37 642 679.516417311854 -37.5164173118544 38 643 655.25642164512 -12.2564216451195 39 718 745.510259465764 -27.5102594657638 40 654 629.568759003626 24.4312409963743 41 632 702.530229132909 -70.530229132909 42 731 735.916503977154 -4.91650397715351 43 392 424.459500568165 -32.4595005681648 44 344 396.630207466584 -52.6302074665843 45 792 802.07951356796 -10.0795135679596 46 852 820.074808518092 31.9251914819075 47 649 657.794886516862 -8.79488651686172 48 629 625.247271541282 3.75272845871757 49 685 695.338970803475 -10.3389708034748 50 617 651.117461674807 -34.117461674807 51 715 670.840618596621 44.1593814033786 52 715 729.229669035365 -14.2296690353646 53 629 657.137474674602 -28.1374746746018 54 916 838.23894913715 77.7610508628499 55 531 494.843524189069 36.1564758109313 56 357 383.17587454737 -26.1758745473697 57 917 863.148164239961 53.8518357600385 58 828 850.53580521513 -22.5358052151305 59 708 701.563558855188 6.43644114481169 60 858 812.738840805526 45.2611591944736 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.252757324926602 0.505514649853203 0.747242675073398 18 0.162187422821915 0.324374845643831 0.837812577178085 19 0.081938593211143 0.163877186422286 0.918061406788857 20 0.0663863315609032 0.132772663121806 0.933613668439097 21 0.0407390878671255 0.081478175734251 0.959260912132874 22 0.0440212347972781 0.0880424695945562 0.955978765202722 23 0.134988667758698 0.269977335517395 0.865011332241302 24 0.0910027926179973 0.182005585235995 0.908997207382003 25 0.166275120793509 0.332550241587017 0.833724879206491 26 0.138431507798851 0.276863015597703 0.861568492201149 27 0.185542499823062 0.371084999646125 0.814457500176938 28 0.132387235321559 0.264774470643117 0.867612764678441 29 0.433300207748441 0.866600415496883 0.566699792251559 30 0.392804851252735 0.78560970250547 0.607195148747265 31 0.39306695627379 0.78613391254758 0.60693304372621 32 0.506774322066487 0.986451355867026 0.493225677933513 33 0.41696111583734 0.83392223167468 0.58303888416266 34 0.399253283875978 0.798506567751955 0.600746716124022 35 0.374924117873337 0.749848235746674 0.625075882126663 36 0.372555430936413 0.745110861872825 0.627444569063587 37 0.323009669346981 0.646019338693961 0.67699033065302 38 0.311778334798714 0.623556669597428 0.688221665201286 39 0.273975812279960 0.547951624559919 0.72602418772004 40 0.417444338360115 0.83488867672023 0.582555661639885 41 0.447506130709229 0.895012261418458 0.552493869290771 42 0.399682476464726 0.799364952929452 0.600317523535274 43 0.35205342397886 0.70410684795772 0.64794657602114 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 2 0.0740740740740741 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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